INDUSTRIAL  MANAGEMENT  LIBRARY 


GRAPHIC  METHODS 


FOR 


PRESENTING  FACTS 


BY 


WILLARD  C.  BRINTON 


NEW     YORK 

THE    ENGINEERING   MAGAZINE   COMPANY 

19  19 


JVI/^.  I'"J    L.  )t:^/?ARY 


\^ 


Copyright,  1914 
Sy  The  Engineering  Magazine   Company 


MAIN  LIBRAK 


TO  MY  MOTHER 


PREFACE 


IN  the  preparation  of  this  book  there  has  been  a  constant  effort  to  present  the 
subject  to  suit  the  point  of  view  of  the  business  man,  the  social  worker,  and  the 
legislator.  Mathematics  have  been  entirely  eliminated.  Technical  terms  are  used 
practically  not  at  all.  Since  the  readers  whom  it  is  most  desired  to  reach  are  those 
who  have  never  had  any  statistical  training,  consistent  effort  has  been  made  to  keep 
the  whole  book  on  such  a  plane  that  it  may  be  found  readable  and  useful  by  anyone 
dealing  with  the  complex  facts  of  business  or  government.  Though  written  primarily 
for  the  non-technical  man,  it  is  hoped  that  this  book  may,  nevertheless,  prove  con- 
venient to  the  engineer,  the  biologist,  and  the  statistician. 

A  definite  effort  has  been  made  to  produce  a  work  which  can  serve  as  a  hand  book 
for  anyone  who  may  have  occasional  charts  to  prepare  for  reports,  for  magazine 
illustration,  or  for  advertising.  Unfortunately,  there  are  extremely  few  draftsmen 
who  know  how  to  plot  a  curve  or  prepare  any  kind  of  a  chart  from  data  presented  to 
them  in  the  form  of  tabulated  figures.  Most  draftsmen  can  plot  a  curve  if  they  are 
given  the  data  and  an  example  showing  the  general  type  of  chart  desired.  The  execu- 
tive who  desires  a  chart  is  usually  too  busy  to  stand  by  a  draftsman  and  explain 
in  detail  just  how  the  chart  should  be  prepared  as  concerns  those  all  important 
details  of  proportion,  scale,  width  of  line,  etc.  It  is  believed  that  the  owner  of  this 
book  will  find  it  feasible  to  run  through  the  various  chapters  and  pages  until  he  finds 
a  chart  most  nearly  like  that  which  he  desires  to  have  made  from  his  own  data. 
A  sample  chart  placed  before  any  draftsman  of  average  ability  should  give  the  drafts- 
man practically  all  the  instruction  needed  for  the  preparation  of  a  similar  chart  from 
other  data. 

Much  careful  labor  has  been  expended  in  so  arranging  the  book  that  a  busy 
reader  may  get  the  gist  of  the  matter  by  looking  at  the  illustrations  and  reading  only 
the  titles  and  the  sub-titles.  The  main  title  under  each  illustration  is  intended  to 
show  exactly  what  the  chart  represents,  just  as  if  it  were  used  in  some  publication  re- 
lating to  the  particular  subject  matter  of  the  chart.  The  sub-titles  relate  to  method 
and  give  criticism  of  each  chart  as  a  whole.  Though  the  text  gives  much  more  de- 
tailed information  concerning  method  than  can  possibly  be  put  into  any  sub-titles,  the 
reader  who  examines  only  the  illustrations  and  the  titles,  without  any  reference  to 
the  text,  will  undoubtedly  get  a  major  portion  of  the  vital  material  in  the  book.  It  is 
believed  that  an  average  reader  may  go  through  the  illustrations  and  the  titles  in 
about  one  hour. 


VI  GRAPHIC   METHODS 

Many  of  the  illustrations  which  have  been  borrowed  for  use  in  this  book  are 
criticized  adversely.  It  is  the  hope  that  all  such  criticisms  will  be  accepted  as  an 
honest  attempt  toward  an  advance  in  the  art  of  showing  data  in  graphic  form.  In 
fairness  to  the  authors  of  those  charts  which  are  criticized,  it  must  be  said  that  there 
has  been  a  very  rapid  advance  in  the  art  of  graphic  presentation  within  the  last  few 
years  and  that  many  of  these  men  would  not  present  the  material  to-day  by  the 
methods  which  may  have  been  used  some  years  ago  in  the  preparation  of  certain 
charts  shown  here.  Where  charts  are  used  and  criticized  adversely,  the  charts  have 
been  included  only  because  it  is  felt  that  they  show  a  practice  which  is  rather  common 
but  is  nevertheless  of  questionable  desirability. 

Many  of  the  suggestions  for  standard  practice  contained  in  this  book  should  be 
taken  as  tentative  only.  The  American  Society  of  Mechanical  Engineers  has  invited 
about  fifteen  of  the  chief  American  societies  of  national  scope  to  co-operate  by  sending 
one  member  each  to  a  Joint  Committee  on  Standards  for  Graphic  Presentation. 
Though  this  committee  is  not  yet  completely  organized,  and  it  will  be  some  time  before 
any  report  is  available,  the  reader  who  desires  further  information  regarding  standard 
practice  should  be  on  the  lookout  for  any  reports  which  the  joint  committee  may 
publish  in  the  future. 

This  volume  may  arouse  in  the  minds  of  many  readers  a  desire  for  more  detailed 
information  than  can  possibly  be  given  here.  The  following  books  are  suggested 
for  the  person  who  wishes  to  take  up  the  study  of  statistics  as  related  to  the  collection 
and  interpretation  of  data  without  special  reference  to  the  methods  of  graphic  pres- 
entation. The  present  work  is  necessarily  limited  to  the  consideration  of  graphic 
presentation,  and  those  who  wish  to  go  further  in  the  general  subject  of  statistics 
should  by  all  means  consult  books  of  the  type  exemplified  by  "The  Elements  of 
Statistical  Method,"  by  Willford  I.  King,  The  Macmillan  Company,  New  York; 
"An  Introduction  to  the  Theory  of  Statistics,"  by  G.  Udny  Yule,  Griffin  and  Com- 
pany, London;  ''Elements  of  Statistics,"  by  Arthur  L.  Bowley,  Charles  Scribner's 
Sons,  New  York;  "Primer  of  Statistics,"  by  W.  Palin  Elderton  and  Ethel  M.  Elderton, 
Adam  and  Charles  Black,  London;  "Statistical  Averages,"  by  Franz  Zizek,  Henry 
Holt  and  Company,  New  York;  "Statistical  Methods  with  Special  Reference  to 
Biological  Variation,"  by  C.  B.  Davenport,  John  Wiley  and  Sons,  New  York.  Any 
list  of  this  sort  is,  of  course,  incomplete  and  these  books  are  mentioned  as  only  a  few 
of  those  which  may  be  found  useful  to  supplement  the  study  of  the  subject  considered 
in  this  volume. 

Part  of  the  matter  here  presented  was  given  in  lectures  delivered  at  the  Graduate 
School  of  Business  Administration  of  Harvard  University,  the  Amos  Tuck  School 
of  Administration  and  Finance  of  Dartmouth  College,  the  Northwestern  University 
School  of  Commerce,  and  the  College  of  Commerce  and  Administration  of  the  Uni- 
versity of  Chicago.  Some  of  the  material  was  presented  before  the  American  Society 
of  Mechanical  Engineers  in  New  York.  The  advance  presentation  of  matter  in 
course  of  preparation  for  the  press  was  made  with  the  cordial  assent  and  approval  of 
the  publishers  of  this  work. 

I  am  greatly  indebted  to  Mr.  Edward  Scott  Swazey,  Mr.  Curtis  Prout,  and  Miss 
Katherine  Tyng,  for  valuable  assistance  and  suggestions  received  during  the  prep- 
aration of  this  book.     Chapter  XV  is  largely  based  on  an  article  prepared  at  the 


PREFACE  Vll 

suggestion  of  the  author  by  Mr.  Pierpont  V.  Davis  of  New  York  City  and  pubUshed 
by  Mr.  Davis  in  Moody's  Magazine.  I  wish  also  to  express  my  thanks  to  numerous 
friends  who  have  given  excellent  suggestions  and  criticisms  during  the  time  the 
manuscript  was  in  preparation. 

If  this  book  should  receive  any  commendation,  much  of  that  commendation  will 
be  the  result  of  good  fortune  in  securing  an  unusually  high  grade  of  drafting  skill  on 
those  charts  which  are  original. 

The  author  cannot  be  responsible  for  the  accuracy  of  the  data  presented  in  many  of 
the  charts  shown.  The  illustrations  have  been  selected  partly  on  account  of  the 
educational  value  of  the  facts,  but  chiefly  because  of  the  methods  used  in  presentation. 
Though  great  care  has  been  exercised  to  make  the  titles  complete,  the  elaboration 
of  titles  beyond  their  wording  in  the  original  source  may  have  resulted  in  some  in- 
accuracies. 

As  far  as  the  author  is  aware,  there  is  no  book  published  in  any  language  covering 
the  field  which  it  has  been  attempted  to  cover  here.  If  the  presentation  of  the 
subject  appears  to  be  crude  and  incomplete,  it  is  hoped  that  any  critic  will  keep  in 
mind  that  there  is  little  precedent  for  guidance  in  a  territory  so  unexplored. 

It  is  impossible  entirely  to  avoid  errors  in  any  book  containing  as  much  detail  as 
results  here  from  the  numerous  complex  illustrations  and  the  necessity  of  carefully 
worded  language  to  give  condensed  information.  Any  corrections,  criticisms  or 
suggestions  will  be  appreciated  by  the  author. 

WiLLARD    C.    BrINTON 

New  York,  June,  1914 


CONTENTS 


Chapter  I.  Component  Parts 1 

The  need  for  graphic  methods  in  presenting  facts.  The  method  of  pres- 
entation as  important  as  the  data.  PossibiHty  for  standard  methods  of 
presentation.  Tabulated  figures  versus  graphic  methods.  A  total  shown 
with  its  component  parts.  The  horizontal  bar.  The  circle  and  sectors. 
Subdivision  of  components.  Separate  bars  totalling  100  per  cent.  Charts 
giving  numerous  subdivisions.  Organization  charts.  Routing  charts 
for  manufacturing  plants  and  offices. 

Chapter  II.     Simple  Comparisons 20 

EiTors  due  to  comparing  by  areas  or  by  volumes  instead  of  by  one 
dimension  only.  The  use  of  graphic  methods  in  geography  books.  The  data 
should  be  shown  on  the  face  of  each  chart  if  possible.  Good  and  bad 
methods  of  including  the  data.  "Eye-catchers"  to  attract  the  attention 
of  the  reader.  Criticisms  of  methods  commonly  used.  Certain  bars 
made  especially  prominent.  Increases  and  decreases.  Lines  connecting 
different  bars.     Examples  of  various  good  methods. 

Chapter  III.     Simple  Comparisons  Involving  Time 36 

Impossibility  of  accurate  interpretation  when  circles  of  different  size  are 
compared.  Errors  when  pictures  of  the  human  figure  in  difl^erent  size  are 
compared.  Methods  which  are  popular  and  accurate  as  well.  Examples  of 
bad  practice  in  arrangement  and  the  same  data  correctly  represented. 
Vertical  bars  giving  the  general  effect  of  a  simple  curve.     Curve  plotting. 

Chapter  IV.     Time  Charts 53 

Horizontal  bars  drawn  to  a  scale  of  time.  Complex  time  charts  by  which 
the  relations  of  numerous  horizontal  bars  may  be  studied.  Time  charts 
showing  bars  combined  with  a  curve  expressing  totals.'  Curves  to  study 
whether  time  schedules  are  maintained.  Rank  charts  to  portray  the  rank  of 
different  individuals  at  various  times.  Rank  charts  showing  actual  rela- 
tive rank  at  any  time  and  also  changes  in  rank  at  various  times.  Train- 
dispatching  charts.     Time-distance  curves. 


GRAPHIC    METHODS 


Chapter  V.     Curve  Plotting 69 

The  desirability  of  using  only  well-known  methods  of  presentation. 
Curves  permit  a  more  rapid  and  more  accurate  interpretation  than  possible 
by  other  methods.  Studies  of  the  causes  of  crests  and  valleys  of  curves. 
Curves  especially  needed  for  complex  data.  The  use  of  curves  in  advertising. 
Polar  co-ordinates  objectionable  for  presenting  statistical  data.  Examples 
of  good  practice  in  curve  plotting. 

Chapter  VI.     Curve  Plotting  Continued 84 

Independent  and  dependent  variables.  Confusion  caused  if  the  inde- 
pendent variable  is  not  used  for  the  horizontal  scale.  Examples  showing 
correct  arrangement  of  scales.  Curves  to  advertise  newspaper  circulation. 
Curve  charts  combining  much  complex  information.  The  use  of  two  sets  of 
co-ordinate  ruling  for  the  vertical  scale.  Moving  averages.  Smoothing 
curves.  Index  numbers.  Weighted  averages.  Curve  studies  of  national 
prosperity. 

Chapter  VII.     Comparison  of  Curves 107 

Similarity  and  contrast  of  curves  plotted  in  the  same  field.  The  zero 
of  the  vertical  scale  should  be  shown  on  the  chart.  Advantages  of  plotting 
curves  for  different  years  one  above  the  other  for  comparison.  Contrast 
in  shape  of  curves  plotted  in  separate  fields.  Advantage  from  shading  the 
space  under  a  curve.  Numerous  dissimilar  but  related  curves  on  the  same 
sheet.  Errors  resulting  if  curves  not  having  the  same  zero  line  are  compared. 
A  total  curve  plotted  from  several  other  curves.  Inverse  relations,  one  curve 
trending  downward  when  another  trends  upward.  Study  of  correlation 
by  plotting  a  curve  from  the  data  of  two  other  curves.  The  angle  of  a  curve 
on  ordinary  rectangular  co-ordinates  tells  nothing  about  the  percentage  rate 
of  growth.  Disadvantages  of  the  arithmetical  scale  ruling  for  curve 
plotting.  Advantages  obtained  by  plotting  curves  on  logarithmically  ruled 
paper. 

Chapter  VIII.     Component  Parts  Shown  by  Curves 138 

Use  of  vertical  bars  with  components  totalling  100  per  cent.  Shaded 
area  under  a  curve  when  the  height  of  the  total  field  represents  100  per 
cent.  The  use  of  several  areas  in  a  curve  field  which  totals  100  per  cent, 
in  height.  A  contrasting  method  of  showing  all  curves  plotted  separately 
but  from  the  same  zero  line.  Universal  co-ordinate  paper  for  convenience 
in  curve  plotting.  Total  curves  with  component  areas  so  that  any  point  on 
a  curve  totals  100  per  cent  for  the  height  of  the  areas  beneath. 

Chapter  IX.     Cumulative  or  Mass  Curves 149 

Factory  production  schedules  and  actual  outputs  plotted  on  a  cumulative 
basis.  Curves  for  income  and  expense  on  a  cumulative  basis.  Various  uses 
for  cumulative  curves.     Cumulative  curves  with  lines  drawn  to  show  rate 


CONTENTS  XI 


of  change.  A  grand  total  cumulative  curve  plotted  from  several  other 
cumulative  curves.  Cumulative  curves  for  the  determination  of  storage 
requirements  for  water  supplies. 

Chapter  X.     Frequency  Curves.     Correlation 164 

The  arrangement  of  objects  so  that  their  position  shows  a  crude  frequency 
curve.  Vertical  bars  to  represent  frequency.  Frequency  curves.  The 
"mode."  Frequency  curves  much  easier  to  interpret  than  charts  using 
bars  or  areas.  Cumulative  frequency  curves.  The  use  of  cumulative 
frequency  curves  for  business  problems.  Cumulative  frequency  curves 
preferably  plotted  on  a  "more  than"  basis  instead  of  on  a  "less  than" 
basis.  Necessity  for  making  the  independent  variable  the  horizontal 
scale.  Wage  comparisons  for  industrial  work.  Studies  of  the  percentage  of 
clerical  work  and  percentage  of  revenue  from  orders  of  various  sizes.  Pin 
boards  to  record  costs  of  doing  work  on  orders  of  different  size.  Theoretical 
curves  for  percentage  of  clerical  work  and  percentage  of  revenue  from 
orders  of  different  size.  The  Lorenz  curve.  Correlation  curves.  "Shot- 
gun" diagrams.  Plotting  curves  to  represent  numerous  points.  Shaded 
areas  to  represent  numerous  dots.  Correlation  charts  for  two  independent 
variables.     Isometrically  ruled  paper  for  chart  work. 

Chapter  XI.     Map  Presentations 208 

Map  presentation  of  prime  importance.  Shading  of  different  areas.  The 
Ben  Day  method  of  mechanical  shading.  Lines  of  equality.  Profiles. 
Maps  with  circles  or  dots  representing  quantities.  Shaded  areas  with  a 
key  to  represent  quantity.  Miscellaneous  methods.  Map  charts  showing 
traflBc.     Map  models  with  built  up  strips  to  show  quantities. 

Chapter  XII.     Maps  and  Pins  . 227 

Map  tacks  projecting  above  the  map.  Map  pins  pushed  in  till  the  heads 
touch  the  map.  Photographing  pin  maps.  Mounting  maps  for  use  with 
map  pins.  Wall  maps  for  use  with  pins.  Map  cabinet  systems.  Pin  maps 
for  advertising  work.  Pins  bearing  identifying  numbers.  Spot  maps  to  a 
scale  with  each  dot  representing  some  large  quantity.  Routing  systems. 
Various  types  of  pins  and  beads  available.  Bead  maps  and  their  great 
advantages. 

Chapter  XIII.     Curves  for  the  Executive 254 

Peak-top  curves  versus  flat  tops.  Methods  for  combining  curves  with 
figures  recording  the  data.  Cards  for  plotting  curves  for  operating  records. 
Advantages  of  the  card  method  for  instantaneous  comparison  of  different 
curves.  Typical  operating  curves  for  a  manufacturing  business.  Typical 
records  for  a  selling  organization.  Arrangement  of  the  card  system  for  exten- 
sion with  increase  of  business.  Moving  average  curves  for  operating  re- 
cords.    Record  cards  for  preserving  all  information  regarding  each  curve. 


Xll  GRAPHIC   METHODS 


Chapter  XIV.     Records  for  the  Executive 288 

Need  for  complete  records  in  curve  form  relating  to  all  main  features 
of  a  business.  Curve-card  filing  methods.  Blueprints  from  the  curve 
cards  allow  a  cross-index  of  all  important  operating  curves.  A  complete  rec- 
ord department  for  a  business.  Methods  for  keeping  records  as  used  by- 
various  large  corporations.  The  need  for  education  in  the  interpretation  of 
curves.  Curves  in  conference  meetings  by  using  a  reflecting  lantern  and 
the  curve-record  cards  without  lantern  slides.  Curves  on  swinging-leaf  dis- 
play fixtures. 

Chapter  XV.     Corporation  Financial  Reports. 307 

The  annual  report  of  corporations  not  usually  put  in  form  to  permit 
intelligent  comparison  by  the  stockholders.  Records  of  previous  years 
not  usually  given.  The  number  of  stockholders  constantly  increasing. 
Best  policy  is  to  give  complete  and  clear  information.  Recent  examples 
showing  bad  practice.  Curves  for  the  United  States  Steel  Corporation  as 
a  suggestion  for  the  type  of  chart  to  be  included  in  a  corporation  annual 
report.  Charts  should  be  a  feature  of  the  annual  report  of  every  large 
corporation. 

Chapter  XVI.     General  Methods  .     .  ' 321 

Methods  for  collecting  and  tabulating  data.  Punched-card  sorting 
and  tabulating  machines.  Use  of  tabulating  machines  for  manufacturing 
records  and  for  analyses  of  selling  results.  The  slide  rule  as  a  great  con- 
venience. The  use  and  abuse  of  significant  figures.  Photographic  copying 
of  charts.  Use  of  the  reducing  glass.  Preparation  of  copy  for  the  engraver. 
The  Ben  Day  process.  Charts  for  two  independent  variables.  Card-board 
models.  Solid  models.  The  desirability  of  curves  and  charts  in  political 
campaigns.  The  projecting  lantern  with  charts  for  campaign  purposes. 
Methods  for  presenting  election  returns  to  large  numbers  of  people.  Charts 
in  parades. 

Chapter  XVII.    A  Few  Cautions 344 

The  importance  of  clear  and  accurate  titles.  Symbols  which  are  easily 
remembered.  No  necessity  for  plotting  curves  vertically.  Errors  resulting 
in  interpretation  of  curves  if  the  zero  of  the  vertical  scale  is  not  shown  on 
the  chart.  The  selection  of  scales  for  curve  plotting.  Different  impressions 
from  curves  from  the  same  data  but  with  various  scales.  Optical  illusions 
which  may  affect  graphic  work.  A  checking  list  for  final  inspection  of 
graphic  presentations.  Need  for  standard  rules  of  grammar  for  the  graphic 
language.  A  few  suggested  rules  for  graphic  presentation.  Great  ad- 
vantages may  result  if  graphic  methods  are  more  widely  used  for  portray- 
ing quantitive  facts. 


GRAPHIC  METHODS 

FOR 
PRESENTING  FACTS 


GRAPHIC    METHODS    FOR 
PRESENTING    FACTS 


Chapter  I 
COMPONENT  PARTS 

AFTER  a  person  has  collected  data  and  studied  a  proposition 
with  great  care  so  that  his  own  mind  is  made  up  as  to  the  best 
solution  for  the  problem,  he  is  apt  to  feel  that  his  work  is  about 
completed.  Usually,  however,  when  his  own  mind  is  made  up,  his 
task  is  only  half  done.  The  larger  and  more  difficult  part  of  the  work 
is  to  convince  the  minds  of  others  that  the  proposed  solution  is  the 
best  one — that  all  the  recommendations  are  really  necessary.  Time 
after  time  it  happens  that  some  ignorant  or  presumptuous  member 
of  a  committee  or  a  board  of  directors  will  upset  the  carefully -thought- 
out  plan  of  a  man  who  knows  the  facts,  simply  because  the  man  with 
the  facts  cannot  present  his  facts  readily  enough  to  overcome  the 
opposition.  It  is  often  with  impotent  exasperation  that  a  person 
having  the  knowledge  sees  some  fallacious  conclusion  accepted,  or 
some  wrong  policy  adopted,  just  because  known  facts  cannot  be  mar- 
shalled and  presented  in  such  manner  as  to  be  effective. 

Millions  of  dollars  yearly  are  spent  in  the  collection  of  data,  with 
the  fond  expectation  that  the  data  will  automatically  cause  the  cor- 
rection of  the  conditions  studied.  Though  accurate  data  and  real 
facts  are  valuable,  when  it  comes  to  getting  results  the  manner  of 
presentation  is  ordinarily  more  important  than  the  facts  themselves. 
The  foundation  of  an  edifice  is  of  vast  importance.    Still,  it  is  not  the 

1 


2  '     ^    , ,     '^        ,  GRAPHIC    METHODS 

foundation  but  the  structure  built  upon  the  foundation  which  gives 
the  result  for  which  the  whole  work  was  planned.  As  the  cathedral 
is  to  its  foundation  so  is  an  effective  presentation  of  facts  to  the  data. 

We  daily  see  facts  presented  in  the  hope  of  creating  interest  and 
action  for  some  really  worthy  piece  of  work  to  benefit  the  people  as 
a  whole.  In  many  of  these  cases  the  attitude  of  the  person  presenting 
the  matter  seems  to  be  that  the  facts  will  speak  for  themselves  and  that 
they  need  little  or  no  assistance.  Ordinarily,  facts  do  not  speak  for 
themselves.  When  they  do  speak  for  themselves,  the  wrong  conclu- 
sions are  often  drawn  from  them.  Unless  the  facts  are  presented  in  a 
clear  and  interesting  manner,  they  are  about  as  effective  as  a  phono- 
graph record  with  the  phonograph  missing. 

If  it  were  more  generally  realized  how  much  depends  upon  the 
method  of  presenting  facts,  as  compared  with  the  facts  themselves, 
there  would  be  a  great  increase  in  the  use  of  the  graphic  methods  of 
presentation.  Unlimited  numbers  of  reports,  magazines,  and  news- 
papers are  now  giving  us  reams  of  quantitative  facts.  If  the  facts 
were  put  in  graphic  form,  not  only  would  there  be  a  great  saving  in 
the  time  of  the  readers  but  there  would  be  infinite  gain  to  society, 
because  more  facts  could  be  absorbed  and  with  less  danger  of  mis- 
interpretation. Graphic  methods  usually  require  no  more  space  than  is 
needed  if  the  facts  are  presented  in  the  form  of  words.  In  many 
cases,  the  graphic  method  requires  less  space  than  is  required  for  words 
and  there  is,  besides,  the  great  advantage  that  with  graphic  methods 
facts  are  presented  so  that  the  reader  may  make  deductions  of  his 
own,  while  when  words  are  used  the  reader  must  usually  accept  the 
ready-made  conclusions  handed  to  him. 

In  many  presentations  it  is  not  a  question  of  saving  time  to  the 
reader  but  a  question  of  placing  the  arguments  in  such  form  that  re- 
sults may  surely  be  obtained.  For  matters  affecting  public  welfare, 
it  is  hard  to  estimate  the  benefits  which  may  accrue  if  a  little  care  be 
used  in  presenting  data  so  that  they  will  be  convincing  to  the  reader. 
If  the  average  citizen,  and  especially  the  business  man,  knew  how  to 
interpret  charts  and  curves,  it  would  be  feasible  to  convey  to  him  in 
effective  form  those  facts  relating  to  broad  public  improvements, 
public-service  operation,  and  national.  State,  or  municipal  manage- 
ment, which  might  affect  the  whole  fabric  of  our  civilization.  Archi- 
medes wanted  only  a  fulcrum  for  his  lever  and  he  would  move  the 
world.    If  the  world  is  ever  moved  it  will  probably  be  by  facts  properly 


COMPONENT    PARTS  3 

presented.  The  method  of  presentation  is  the  fulcrum  without  which 
facts,  as  a  lever,  are  useless. 

The  preparation  and  interpretation  of  simple  charts  and  curves 
should  be  taught  in  the  public  schools  as  a  part  of  arithmetic.  The 
work  of  kindergarten  nature  now  done  in  the  lower  grades  of  the 
public  schools  could  very  readily  be  extended  so  that  the  pupils  would 
be  making  charts  and  curves  without  realizing  that  the  work  (or  play) 
had  any  relation  to  mathematics.  Text-books  for  geography  are  al- 
ready making  effective  use  of  charts.  In  the  public  schools  of  Newark 
and  of  Trenton,  New  Jersey,  grammar-school  pupils  are  preparing 
charts  and  plotting  curves  relating  to  records  which  show  the  present 
condition  and  recent  development  of  their  home  city.  The  principles  of 
charting  and  curve  plotting  are  not  at  all  complex,  and  it  is  surprising 
that  many  business  men  dodge  the  simplest  charts  as  though  they 
involved  higher  mathematics  or  contained  some  sort  of  black  magic. 

If  an  editor  should  print  bad  English  he  would  lose  his  position. 
Many  editors  are  using  and  printing  bad  methods  of  graphic  presenta- 
tion, but  they  hold  their  jobs  just  the  same.  The  trouble  at  present 
is  that  there  are  no  standards  by  which  graphic  presentations  can  be 
prepared  in  accordance  with  definite  rules  so  that  their  interpretation 
by  the  reader  may  be  both  rapid  and  accurate.  It  is  certain  that 
there  will  evolve  for  methods  of  graphic  presentation  a  few  useful 
and  definite  rules  which  will  correspond  with  the  rules  of  grammar 
for  the  spoken  and  written  language.  The  rules  of  grammar  for  the 
Enghsh  language  are  numerous  as  well  as  complex,  and  there  are  about 
as  many  exceptions  as  there  are  rules.  Yet  we  all  try  to  follow  the  rules 
in  spite  of  their  intricacies.  The  principles  for  a  grammar  of  graphic 
presentation  are  so  simple  that  a  remarkably  small  number  of  rules 
would  be  sufficient  to  give  a  universal  language.  It  is  interesting  to 
note,  also,  that,  there  are  possibilities  of  the  graphic  presentation  be- 
coming an  international  language,  like  music,  which  is  now  written 
by  such  standard  methods  that  sheet  music  may  be  played  in  any 
country. 

With  oral  and  written  language  and  with  tabulated  figures  also  the 
reader  sometimes  draws  conclusions  regarding  the  relative  importance 
of  different  things  from  the  comparative  length  of  time  or  amount  of 
space  used  in  presentation.  Graphic  methods  overcome  this  difficulty 
by  showing  quantitative  facts  in  true  proportions  which  give  instantly 
the  correct  interpretation.     In  tabulations  like  that  on  page  4  it  is  only 


4  GRAPHIC    METHODS 

the  highly  skilled  reader  who  can  refrain  from  regarding  the  five  differ- 
ent items  listed  as  of  somewhere  nearly  equal  numerical  importance, 
simply  because  the  five  different  items  are  given  exactly  the  same  space 
and  prominence  when  written  down  on  the  page. 

Percentage  of  Each  Race  in  the  Population  of  the  World 

Yellow 45 

White 41 

Black 11 

Brown 2 

Red 1 

It  requires  mental  concentration  in  interpreting  even  these  simple 
figures  to  get  the  correct  impression  of  the  very  large  percentage  of 
the  two  chief  races  and  the  numerical  insignificance  of  the  one  last 
named.  If  these  data  were  shown  in  a  simple  horizontal  bar,  somewhat 
like  that  seen  in  Fig.  1,  the  relative  proportions  of  the  different  races 


a 

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Scale  !"» I  Cent» 

-5  Cent/S 


Fig.  I.    Disposition  of  a  5-cent  Fare  Paid  to  the  Boston  Elevated  Railroad  in  the  Year 

Ending  September  30,  1909 

The  horizontal  bar  gives  an  especially  good  method  for  showing  component  parts 


COMPONENT    PARTS 


would  instantly  be  seen  without  any  mental  effort  on  the  part  of  the 
reader. 

Fig.  1  is  a  very  satisfactory  form  of  chart  to  bring  out  the  component 
parts  of  any  group  total.  The  horizontal  bar  need  be  made  only  wide 
enough  to  show  the  various  kinds  of  shading  necessary  to  give  a  good 
contrast.     Engineering  dimension  lines  above  each  block  in  the  bar  are 


of  great  advantage 
for  convenient  read- 
ing. The  dimension 
lines  permit  of  group- 
ing in  such  a  manner 
that  several  of  the 
detail  blocks  could 
be  included  in  vari- 
ous sets  of  dimension 
lines  to  show  such 
items  as  total  fixed 
charges,  total  operat- 
ing expenses,  etc. 

In  this  type  of 
chart  the  actual 
figures  representing 
the  value  of  the  com- 
ponents should  be 
given  for  the  use  of 
any  reader  who  may 
wish  to  draw  his  own 
conclusions  or  to 
make  new  combina- 
tions of    figures  dif- 


50% 


Fig.  2.    Disposition  of  the  Gross  Revenue  of  the  Bell  Tele- 
phone System  for  the  Year  191 1 

This  chart  was  taken  from  the  annual  report  to  the  stockholders  of  the 
American  Telephone  and  Telegraph  Company  for  the  year  ending 
December  31,  1911 

The  circle  with  sectors  is  not  as  desirable  an  arrangement  as  the  hori- 
zontal bar  shown  in  Fig.  1 


ferent  from  those  shown  in  the  chart.  As  a  general  thing  it  is  always 
desirable  to  have  full  data  given  on  any  chart. .  Fig.  1  gives  all  the  data 
without  in  any  way  detracting  from  the  ease  of  reading  the  chart  itself. 
It  would  be  desirable  to  have  a  large  number  of  the  illustrations 
in  this  book  printed  in  color.  Charts  which  are  made  in  color  can  read- 
ily bring  out  points  which  are  not  easily  portrayed  when  only  black  ink 
is  used.  The  reader  should  keep  in  mind  for  his  own  work  that  he 
should  use  colors  in  making  those  charts  where  colors  are  economically 
possible.     For  the  purpose  of  this  book,  color  printing  is  prohibitive 


6 


GRAPHIC    METHODS 


on  account  of  the  cost.  In  printed  reports,  in  magazine  articles,  and 
in  magazine  advertising,  color  printing  is  not  at  the  present  time  com- 
monly available.  The  illustrations  of  this  book  will  accordingly  show 
what  can  be  done  in  printing  complex  charts  with  only  one  color  of  ink, 

under  the  same  conditions 
that  would  be  found  in  the 
preparation  of  material  for 
magazine  articles,  printed 
reports,  and  ordinary  pro- 
spectus or  other  advertis- 
ing matter. 


Fig.  2  is  a  form  of  chart 
used  probably  more  widely 
than  any  other  form  to 
show  component  parts.  The 
circle  with  sectors  is  not  a 
desirable  form  of  presenta- 
tion, however,  because  it 
does  not  have  nearly  such 
flexibility  as  the  method 
shown  in  Fig.  1.  The  sector 
method  does  not  permit  of 
convenient  arrangement  of 
names     for     the     different 


Fig.  3. 


The  Survey 

Disposition  of  a  Family  Income  of  from 
$900  to  $1000 

This  cut  shows  an  attempt  to  put  figures  in  popular  form. 
The  eye  is  likely  to  judge  by  the  size  of  the  pictures  rather 
than  by  the  angles  of  the  sectors 


components.  Note  that  the  direction  of  the  lettering  must  be  reversed 
as  the  eye  proceeds  around  the  circle.  In  this  case,  "Interest  and 
Dividends"  reads  upward  while  "Materials,  Rents,  Traveling  Ex- 
penses, etc."  reads  downward.  Another  disadvantage  of  the  sector 
method  is  the  impossibility  of  placing  figures  in  such  manner  that  they 
can  be  easily  compared  or  added.  The  horizontal-bar  method  permits 
of  placing  figures  so  as  to  keep  the  decimal  points  in  line,  thus  making 
it  possible  to  add  the  whole  column  of  figures  relating  to  the  various 
components. 

The  sector  method  is  probably  so  widely  known  through  presentation 
in  exhibits,  illustrations  for  popular  magazines,  etc.,  that  it  is  more 
generally  understood  than  any  other  method  now  in  use.  The  more 
easy  reading  of  the  wedge  or  sector  chart  is,  however,  largely  due  to 
habit.  If  the  horizontal-bar  method  of  Fig.  1  were  used  as  frequently 
as  the  sector  method,  it  would  be  found  in  every  way  more  desirable 


COMPONENT    PARTS 


than  the  sector  method  and  would,  in  a  very  short  time,  become  so  well 
known  that  it  would  be  read  much  more  quickly  and  accurately  than 
the  method  involving  sectors. 

In  Fig.  4  a  double  scale  is  used  by  which  the  same  data  can  be 
mterpreted  from  two  different  standpoints.  On  the  left  the  scale  is 
given  in  millions  of  tons,  and  on 
the  right  in  millions  of  dollars. 
The  reader  can  interpret  the  chart 
from    whichever    standpoint     he 


M  .  '  '  '  ' . '     ■ 

5     jirflCT  in  THt  FORM  OF  UNCONSWHrO  FUEt  IM  TMC 
'  CmOEBS  l»NO  S(»ABKS 


_■ 


.  U>ST  tN  OASES  OfSCHAHOEO  FRpM  STACK 


LOST  IN  VAPORIZING  MOISTURE  IN  COAL 


lOO  5 


so  o 

3 


UTICIZEO  8Y  eoiUEfi 


prefers.  Though  this  chart  is  ar- 
ranged vertically  instead  of  hori- 
zontally, it  really  makes  little 
difference  which  way  the  bars  are 
placed.  As  a  general  thing,  the 
horizontal  arrangement  lends  itself 
more  readily  to  the  use  of  type  so 
that  the  reader  may  read  type 
statements  without  having  to  turn 
the  book. 

In  Fig.  5  the  whole  population 
of  the  United  States  is  divided  first 
into  native  white,  foreign  white, 
.and  colored,  then  each  of  these 
groups  is  subdivided  according  to 
place  of  birth.  This  is  an  excellent 
type  of  chart  to  use  if  subdivi- 
sions in  the  component  parts  of 
any  unit  have  to  be  shown.  If  the 
scale  to  which  the  chart  is  drawn 
is  specified,  it  is  possible  for  the 
reader  to  measure,  with  an  ordi- 
nary ruler  or  with  an  engineer's 
scale,  the  exact  percentage  size  of 
each  of  the  different  components. 

If  the  chart  is  made  on  co-ordinate  paper  with  ruled  squares,  the 
reader  can  obtain  the  size  of  each  component  direct  from  the  co-ordinate 
lines.  The  trouble,  however,  with  using  co-ordinate  paper  for  charts 
of  this  sort  is  that  the  components  are  likely  to  begin  and  end  at  points 
not  falling  upon  the  co-ordinate  lines,  thus  making  it  necessary  to  count 


iOm-THROUQHIIAetA'riON.I^AKAQE  OF  STEAM   CTC 


LOST  THROUGH  UNCONSUMEO  FUEL  IN  ASH 


CONSUWEO  IN  STAJITJfJG  FlO^S, 

KCrPlKTO  f  ►KSINE  HOT  WHILE  STAKtOIMC^ 

AND  LEFT  Mi  FlRt  SOfJlT  CNDOP  RUH^EaTlHATto) 


20 


Adapted  from  Data.  Chicago 

Fig.  4.  Utilization  and  Accompanjdng 
Wastes  of  One  Year's  Coal  Supply  for 
Locomotives  on  Railroads  of  the 
United  States 

The  double  scale  permits  reading  this  chart  in  tons 
or  in  dollars 


8 


GRAPHIC    METHODS 


fractions  of  a  division  at  both  beginning  and  end  of  the  component 
to  be  measured.  The  best  thing  in  charts  of  this  kind  is  to  use  unruled 
paper,  and  specify  the  scale.  The  reader,  if  he  wants  the  exact  data,  can 
take  his  measurements  with  a  ruler.  The  engineer's  scale  has  its  sub- 
divisions in  decimals  and  hence  is  the  most  convenient  scale  for  chart 
work.  An  engineer's  scale  should  be  part  of  the  equipment  of  every 
person  who  has  charts  to  make. 

Another  method  of  showing  the  relative  size  of  the  divisions  and  sub- 
divisions of  a  unit  or  group  is  shown 
in  Fig.  6.  In  this  case  we  have  the 
total  population  of  the  United  States 
split  into  its  component  groups  accord- 
ing to  the  condition  in  regard  to  mar- 
riage. The  subdivision  bars,  given  be- 
low the  total  bars,  show  the  conjugal 
condition  in  each  of  the  main  groups 
which  enter  into  the  total  population. 
Each  of  these  main-group  bars  is  cross- 
hatched  to  show  the  conjugal  condition 
within  the  group.  The  combined  length 
of  the  four  bottom  bars  is  equal  to  the 
length  of  the  total -population  bar 
shown  at  the  top.  These  same  data 
could  have  been  presented  by  the 
method  shown  in  Fig.  5.  It  will  be 
noted,  however,  that  in  Fig.  6  all  the 
figures  have  been  included,  and  are 
available  for  reference  purposes  with- 
out detracting  from  the  utility  of  the  chart  itself.  The  lettering  was 
done  by  hand  and  shows  the  possibilities  for  neatness  resulting  from 
hand  work  when  a  skilled  draftsman  is  employed.  In  many  ways  the 
method  of  Fig.  5  is  preferable,  but  it  is  probably  true  that  Fig.  6 
would  be  more  readily  understood  by  the  average  untrained  reader. 

Where  there  are  a  large  number  of  items  to  be  compared  and  the 
components  of  each  item  are  given,  the  method  of  Fig.  7  is  n  very 
convenient  one.  The  Census  Atlas  for  the  1900  Census  contained 
many  pages  of  charts  of  this  type  for  its  comparisons  of  different  States. 
By  placing  bars  for  all  the  States  on  one  page,  the  total  for  the  country 
is  shown  as  100  pej  cent  in  the  vertical  direction.     No  vertical  scale 


9  ,    t    I    i-SP  Scale  fo  inch  equals  5  percent 

United  States  Statistical  Atlas  for  the  Census  of  1900 

Fig.  5.     Elements  of  the  Population 
of  the  United  States  in  1900 

Here  the  components  of  the  total  population 
are  shown  in  their  relative  sizes  on  the 
vertical  scale.  Each  component  is  also 
divided  into  different  subdivisions  whose 
percentage  size  may  be  read  from  the 
horizontal  scale.  This  is  an  admirable 
method  of  presentation  if  components 
must  be  subdivided 


COMPONENT    PARTS 


TOTAL  Population.  .76,303,387 


N*Tivc  White    40  949,362 

Native  Parents 


■'■■■■*!k — •^■-   ^  "  m^s 


i'  pAJigggg 


?  24,3S4.3e 


NATiVE_jWMITC 

FOREiCN  "^Parents 


.  .  .15.647.017 


M'lTjiAojoj'; 

VM.1 19,670 


I  Married 

^^^^      WlOOWEO 


i 

FbREION    WHITE 10.21  3. ei7  f,  6.211.278 


■*--1.O£9.035  ^ 


NEORO 8,634,094 


Fig.  6.     Conjugal  Condition  of  the  Population  of  the  United  States  in  1900 

The  four  lower  bars  show  components  of  the  total  population  represented  by  the  upper  bar.     The  combined 
length  of  the  four  lower  bars  equals  the  length  of  the  upper  bar 

is  used,  all  the  bars  being  made  of  equal  width.  In  this  particular 
case  (Fig.  7)  we  have  a  total  split  into  its  components  and  again  sub- 
divided so  as  to  show  the  prevalence  of  a  second  factor  which  is  in- 
cluded in  the  first.  Thus,  we  see  the  proportion  of  illiterates  in  each 
of  the  main  groups  of  population  for  each  State.  x\ll  of  the  States 
are  shown  on  the  same  basis,  since  all  are  depicted  by  bars  of  the  same 
length  representing  100  per  cent.  It  is  not  easy  to  make  a  clear  black- 
and-white  drawing  if  one  kind  of  cross-hatching  must  be  placed  on 
top  of  another  kind.  Fig.  7  shows  that  it  is  possible,  however,  to 
superimpose  tw^o  kinds  of  cross-hatching  and  get  a  drawing  that 
is  fairly  clear.  The  facts  in  this  chart  would  have  been  brought  out 
better  if  colors  had  been  used  for  the  main  divisions  of  population. 
Ruled  cross-hatching  in  black  to  represent  the  percentages  of  illit- 

New  York 


North  Dakota 


West  Virginia 


Qs-a/; 


Mississippi 


•<12.4%                                     ^ 

;l|56. 2  %  'lIlJilillpfeM 

Native  White 


;^  Foreign  White 


Negro 


II  iterate 


Fig.  7.     Males  of  Voting  Age  in  certain  States,  in  1900,  by  Color  and  Nativity  and 

by  Illiteracy 

A  method  for  two  successive  divisions  into  components  is  shown  here.     The  proportion  of  illiterates  in  each 
group  is  brought  out  by  the  horizontal  ruling 


erates  would  show  clearly  through 
the  colored  ink  used  for  the  main 
divisions. 

Though  it  would  have  been 
possible  to  portray  the  data  given 
in  Fig.  7  in  the  form  of  the  square 
shown  in  Fig.  5,  the  square  would 
take  up  so  much  room  on  the  page 
that  the  method  would  be  prohib- 
itive if  all  the  States  had  to  be 
shown  on  one  page  for  comparison. 
With  the  method  of  Fig.  7,  it  is 
possible  to  place  on  one  page  all 
the  forty-eight  States  so  that  com- 
parison between  States  can  be 
made  instantly  and  accurately. 

Fig.  8  shows  another  method  of 
analyzing  to  100  per  cent  in  each 
of  two  directions.    The  method  of 
Fig.  5  could  be  used  for  these  data, 
but  would  not  be  as  easy  to  under- 
stand  as   the  method   of   Fig.   8. 
Fig.  5  would  require  most  careful 
cross-hatching  to  bring  out  the  ver- 
tical subdivisions  for  each  of  the 
different    States.      By    using    the 
method  of  Fig.  8,  each  State  can 
be  shown  distinctly  even  if  it  is 
only  the  width  of  a  line,  as  in  the 
case  of  Nevada  or  Wyoming.     The 
wide  space  between  the  different 
bars  showing  the  States  adds  tre- 
mendously to  the  clearness  of  the 
diagram.      The  vertical  scale  for 
the  width  of  bars  is  made  accord- 
ing   to    the    number    of  electoral 
votes   from    each    of    the    States. 
New  York  has  more  electoral  votes 
than  any  other  State,  and  is  there- 

10 


^ 


T*rj  f9oe. ORYM4t9oa. 


MINN.  ry/yy/y////x^\v\\\\\v\\\\\vsk\\\\\\^ 

M.D.      « I 


MASS 


CALir 


Petnn 


Conn    E222ZZZZZSZZ 
Ore:.     ■ c 

N  H  I 


Wise    V//////////y/////////\f~^^\ 
Ida       I 


DOTTED    LINE   DIVIDES  (2)  f 
CEntAGE'  to   the   left,     BRYAN 
HEAVY      LINES    DIVIDE.  ®    PAR 
FROM    THE.    UtFT,     TAFT,     ROOSI 
RE.P.  PR 

V/Mv/M   "^^^m  wmm 


S   IN    I908,TAFT   per- 
TD    THE    RIGHT. 
IE.S   IN    I9I£:,-  BE.GJNHtHO' 
VE.LT.    WILSON. 
>G.  DEM. 


Fig.  8. 


Prof.  IrHng  Fisher  in  the  Mew  York  Times 

The  Vote  for  President  in  1908 
and  in  1912  by  States 

Compare  this  with  Fig.  5  where  the  vertical  scale 
IS  continuous,  without  the  gaps  necessary  here 
in  order  to  distinguish  diflFerent  States. 


COMPONENT    PARTS 


11 


Relations    Between    Annual    Cost    of    Motor    Trucks 
And  Characteristics  of  Service. 


fore  given  greater  width  than  any  other  State  in  proportion  to  the 
greater  size  of  its  electoral  vote.  The  horizontal  division  has  been 
made  according  to  the  percentage  number  of  votes  for  each  of  the 
main  political  parties.  Two  different  elections  are  shown  by  using 
solid  lines  and  dotted  lines.  The  chart  proves  that  the  Democratic 
vote  of  1913  was  essentially  the  same  as  the  Democratic  vote  in  1908, 

and  that  a  Demo- 
crat was  elected 
President  in  1912 
largely  because 
there  were  three 
candidates  in  1912 
and  only  two  in  1908. 
This  is  an  admirable 
piece  of  presentation 
even  though  the 
lettering  and  draft- 
ing are  not  quite  as 
good  as  they  might 
have  been  if  more 
care  had  been  used, 
though  probably  al- 
lowance  must    be 


a)  Character  of  work: 

Size  and  t7pe  of  truck 

Nature  of   ionds 

Number  of  cars..*" 

Distance  per  day 

Number  of  stops  per  day. 
Days  to  service 


b)  Roads  and  climate: 

Road   surface 

Grades   

Otber  street  traffic. 
Climate   


c)  System  of  operating: 

Routing    

Loading  and   unloading. 

Overloading 

Oversoeedlnir    

Oarage    facilities 

Care  of  cars 


Massachusetts  Institute  of  Technology — Vehicle  Research 


Fig.  9. 


The  Factors  Entering  into  the  Annual  Cost  of 
Motor  Trucking  Service 

The  scheme  of  this  convenient  form  of  tabulation  is  somewhat  similar 
to  that  of  Fig.  5.  Here,  however,  the  components  are  only  named 
without  denoting  their  relative  size  or  importance 


made  for  the  limita- 
tions of  paper  and 
presswork  in  daily 
newspaper  printing. 
When  studying  a  number  of  varied  components,  and  the  relations 
of  each  to  every  other  one,  a  chart  like  Fig.  9  is  frequently  of  great 
assistance.  This  chart  shows  that  certain  components  are  affected  by 
features  which  may  not  affect  other  components.  We  have  here  the 
total  cost  of  motor  trucking,  studied  according  to  the  components  of 
the  cost  and  also  according  to  the  conditions  which  produce  those 
.component  costs.  We  may  consider  either  the  service  conditions  or 
the  cost  components.  We  have  100  per  cent  in  the  horizontal  direc- 
tion and  100  per  cent  also  in  the  vertical  direction.  The  total  of  the 
components  in  either  direction  is  100  per  cent,  but  the  actual  size  of 
each  is  not  given  because  the  size  is  not  known  or  because  it  may 
vary  from  time  to  time. 


n 


GRAPHIC    METHODS 


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Fig.  13.     Organization  Chart  of  a  large  Company  Manufacturing  Stoves 

A  complete  organization  chart  should  always  include  the  stockholders  and  the  Board  of  Directors  as  shown 

here 

A  diagram  like  that  of  Fig.  10  may  be  of  considerable  assistance 
if  a  very  complex  relation  of  components  has  to  be  shown.  In  Fig.  9, 
the  components  have  only  one  subdivision.  In  Fig.  10,  however, 
we  have  fuel  cost  subdivided  as  manj^  as  five  different  times.  Though 
the  method  of  Fig.  10  could  easily  be  used  for  the  data  of  Fig.  9,  that 
of  Fig.  9  has  its  advantages  in  that  it  makes  printing  cheaper  and 
is  therefore  desirable  whenever  it  can  be  used.  Fig.  9  can  be  prepared 
on  a  typewriter  or  can  be  set  up  by  any  printer,  while  Fig.  10  requires 
the  making  of  a  drawing. 

In  Fig.  11  the  ramifications  of  the  influence  of  the  J.  P.  Morgan 
Company  and  various  large  banking  concerns  are  shown.  This  chart, 
taken  from  the  Pujo  Money  Report,  was  drawn  originally  in  several 
different  colors  of  ink.  Though  the  windmill  effect  of  the  chart  is 
rather  disagreeable  to  the  eye,  the  chart  nevertheless  shows  the  ap- 
plication of  the  graphic  method  to  such  complex  situations  as  it  is 
almost  impossible  to  portray  with  language  alone. 

Organization  charts  are  not  nearly  so  widely  used  as  they  should 
be.  As  organization  charts  are  an  excellent  example  of  the  division 
of  a  total  into  its  components,  a  number  of  examples  are  given  here 
in  the  hope  that  the  presentation  of  organization  charts  in  convenient 
form  will  lead  to  their  more  widespread  use. 


16  GRAPHIC    METHODS 

It  has  been  well  stated  that  an  organization  chart  closely  resembles 
a  genealogical  tree. 

Authority  reaches  down  through  the  several  branches  of  an  organization  like 
descent  of  blood,  and,  if  properly  planned,  it  will  be  as  irregular  for  a  factor  in  an 
organization  to  be  in  doubt  as  to  the  person  in  authority  over  him  as  for  the  child 
to  deny  the  parentage  of  his  father.  Such  a  chart  should  be  drawn  for  every  or- 
ganization, even  more  especially  for  those  organizations  which  are  short-handed  ex- 
panding businesses  in  which  one  man  holds  the  authority  of  several  positions.  It  should 
be  graphically  shown  what  positions  are  only  temporarily  filled,  so  that  when  new  men 
are  engaged  they  will  fit.  into  the  scheme  with  functions  planned.  Then  there  will 
be  no  irritation,  no  feeling  on  the  part  of  some  that  their  authority  has  been  usurped. 

If  such  a  chart  is  made  there  will  be  fewer  cases  of  conflict  or  of  short-circuiting 
of  orders.  Every  command  from  the  general  that  is  given  directly  to  the  private 
over  the  head  of  the  captain  weakens  the  authority  of  the  captain  over  the  private 
and  weakens  the  authority  of  the  general  over  the  captain.  A  military  organization 
is  so  planned  that  each  man  knows  from  whom  to  take  orders,  but  business  proceeds 
too  much  on  personal  authority.    An  organization  chart  will  help  to  prevent  this. 

Of  course,  no  two  businesses  can  have  identical  organizations.  The  skeleton 
may  be  the  same,  however,  and  just  as  the  proper  study  of  the  functions  of  the  human 
body  begins  with  the  skeleton,  so  the  study  of  organization  should  begin  with  those 
simple  outlines  which  appear,  in  the  main,  in  all  completely  and  successfully  organ- 
ized businesses.  Very  few  enterprises  are  organized  properly.  Very  few  have  an 
organization  that  can  be  charted  at  all.  That  is  one  reason  why  there  is  such  in- 
efiiciency  in  industry. 

As  a  general  thing  it  is  better  to  have  an  organization  chart  begin 
with  the  stockholders  and  then  show  the  board  of  directors  as  inter- 
mediate between  the  stockholders  and  the  president.  In  reality,  a 
typical  organization  chart  represents  the  shape  of  an  hour  glass  or  a 
double  funnel,  with  the  large  number  of  stockliolders  on  one  side  and 
the  large  number  of  employees  on  the  other.  The  board  of  directors, 
the  president,  and  the  officers  of  the  company  are  at  the  narrow  part, 
with  the  president  as  the  intermediary  through  which  all  transactions 
take  place  between  the  large  number  of  stockholders  and  the  large 
number  of  employees. 

The  routing  of  work  through  the  many  processes  and  departments 
of  a  large  plant  is  a  subject  of  such  great  importance  that  charts  are 
frequently  desired  for  the  study  of  such  routing.  Fig.  14  is  a  fairly 
good  example  of  this  class  of  chart.  In  a  complete  chart,  the  depart- 
ments would  of  course  be  designated  for  easy  reference,  by  names, 
numbers,  or  letters.  Colored  ink  could  be  used  to  keep  one  class  of 
work  distinct  from  another.     Colored  inks  would  help  tremendously 


COMPONENT    PARTS 


17 


Fig.  14.    Graphic  Representation  of  Processes  and  Routing  in  a  Representative  Plant 

Names  of  departments  and  operations  are  omitted  by  request  of  the  proprietors  of  the  establishment  in 

which  this  chart  was  made 


18 


GRAPHIC    METHODS 


I  lib 

§"p|-sl 
SI?  31 


vy- 


COMPONENT    PARTS  19 

in  simplifying  Fig.  14,  but  are  not  available  here  because  of  the  pro- 
hibitive expense  of  color  printing.  Colored  drawing  inks  can  be  ob- 
tained at  almost  any  stationery  store.  A  bottle  of  each  color  should 
be  a  part  of  the  equipment  of  any  person  who  is  regularly  doing  chart 
work.  Note  in  Fig.  14  the  small  curves  drawn  where  one  route  line 
crosses  another  line.  By  means  of  small  curves  like  these  it  is  very 
easy  to  keep  the  lines  separate  and  to  show  clearly  that  the  lines 
crossing  each  other  are  entirely  independent. 

Orders  and  other  printed  forms  sent  through  a  large  organization 
must  follow  a  routing  entirely  distinct  from  that  actually  followed 
by  the  heavy  materials.  The  routing  of  printed  forms  in  a  large 
business  is,  in  itself,  a  matter  worthy  of  most  careful  study  to  get  a 
true  understanding  of  their  complex  movements.  A  clear  idea  of 
office  system  is  almost  impossible  unless  the  data  are  charted.  Fig,  15 
may  give  some  suggestions  for  a  chart  to  show  the  movement  of  printed 
forms  through  an  industrial  plant.  Here  again  printing  by  colored 
inks  such  as  would  be  used  on  the  original  drawing  would  be  of  great 
service  in  making  the  chart  easy  to  understand  and  easy  to  follow  from 
department  to  department. 

If  a  building  contains  many  stories  the  routing  diagram  for  mate- 
rials and  also  the  routing  diagram  for  printed  forms  can  be  made 
conveniently  by  a  rough  perspective  drawing  showing  the  different 
floors  as  planes  one  above  the  other.  Colored  ink  lines  on  the 
perspective  chart  will  show  clearl}'  the  movement  of  materials  through 
the  manufacturing  building,  and  will  indicate  the  elevator  movements 
for  material  in  a  manner  not  possible  if  the  departments  are  repre- 
sented all  in  one  plane  on  the  ordinary  sheet  of  paper.  Perspective 
charts  of  floors,  one  above  the  other,  are  so  simply  made  that  their 
advantage  should  not  be  overlooked  when  preparing  routing  charts 
for  plants  having  multi-story  buildings. 


Chapter  II 
SIMPLE  COMPARISONS 

ONE  of  a  business  man's  chief  assets  is  his  abiHty  to  show  things 
to  others  in  their  true  proportions.     He  is  continually  making 
contrasts,  and  holding  up  for  comparison  different  propositions 
which  come  up  in  his  daily  affairs.     The  graphic  method  lends  itself 
admirably  to  use  in  making  comparisons.     It  is  surprising  how  much 
clearer  even  simple  comparisons  of  only  two  or  three  items  will  appear 
when  their  numerical  value  is  put  in  graphic  form  rather  than  in  figures. 
Fig.  16  is  a  cut  taken  from  the  report  of  the  Metropolitan  Sewage 
Commission.    Most  people  know  so  little  about  bacteria  that  it  would 
mean  nothing  to  them  to  say  that  the  Harlem  River  contains  15,600 
bacteria  per  cubic  centimeter  of  water.    When,  however,  such  a  com- 
parison is  made  as  is  shown  in  Fig.  16,  even  the  most  casual  glance 
would  convince  anyone  that  the  Harlem  River  is  not  the  most  ideal 
Bacteria    per    Cubic   Centimeter  of   Water 


I20 

1,600 

I5,600 

Atlantic 

Lower 

Harlem 

Ocean 

New  York 
Bay 

River 

Fig.  1 6.    Bacteria  in  the  Waters  of  New  York  Harbor 

This  illustration  is  taken  from  the  -eport  of  the  Metropolitan  Sewage 
Commission.  The  representation  as  though  seen  through  a  micro- 
scope is  decidedly  effective 

swimming  place.  The  figures  for  the  bacteria  count  are  given  with 
the  chart  so  that  all  the  data  are  available  to  anyone  who  may  wish 
to  study  the  facts  from  a  scientific  standpoint. 

The  drawing  of  Fig.  17  is  of  the  cartoon  type,  effective  for  wall 
exhibitions  or  for  use  in  the  more  popular  magazines.    This  particular 

20 


SIMPLE    COMPARISONS 


n 


Fig.  17. 


The  Independent 

Five  Forms  of  Our  National 
Waste 

A  cartoon  type  of  chart  like  this  will  reach  a 
popular  audience.  Accuracy  of  statement 
should  not,  however,  be  sacrificed  as  it  has 
been  here,  in  that  there  is  no  way  of  correctly 
comparing  the  money  bags 


diagram  contains  nothing  by  which  accurate  comparison  may  be  made. 

No  figures  are  given,  and  it  is  impossible  to  tell  whether  the  different 

money  bags  should  be  compared  on 
the  basis  of  diameter,  area,  or  volume. 
Almost  the  only  conclusion  which 
can  be  drawn  from  such  a  diagram 
is  one  regarding  the  relative  rank  of 
the  different  expenditures.  The  re- 
liability of  even  that  is  likely  to  be 
questioned  because  of  the  evident 
lack  of  accuracy  in  this  kind  of  chart. 
Nevertheless  the  cartoonist  style 
should  not  be  broadly  condemned, 
for  it  has  tremendous  possibilities. 
It  is  possible  to  combine  the  car- 
toonist's wonderful  power  of  arous- 
ing interest  with  methods  of  present- 
ing facts  which  will  give  a  numerical  interpretation  that  cannot  be 

misunderstood.     There  is  a  great  oppor- 
tunity   waiting   for    the    man   who   can 

combine  cartoon  methods  with  accuracy 

of  numerical  statement. 

Fig.  18  gives  a  statement  which  the 

illustration   does   not   support.      In  the 

first  place,  the  dates  of  the  two  years 

compared  are  not  given.     In  the  second 

place,  it  is  impossible  for  the  reader  to 

tell  whether  the  diagram  is  drawn  on  the 

basis  of  one  dimension,  two  dimensions, 

or  three  dimensions.     It  would  be  a  hope- 
less task  to  fit  the  area  of  the  smaller 

washing  machine  into   the   area  of   the 

larger  washing  machine.     Methods  like 

this  cannot  be  too  severely  condemned. 
Commercial  geography,  as  it   is  now 

widely  taught  in  the  public  schools   by 

listing  the  various  imports  and  exports  of 

countries  and  the  products   of  different 

cities,  fails  to  give  a  clear  idea  of   the 


The  sale  of  washing- 
machines  has  increased 
sevenfold  in  the  past 
three  years. 


Good  Housekeeping 

Fig.  18.  Illustration  Intended  to 
Show  that  the  Sale  of  Wash- 
ing Machines  has  Increased 
Sevenfold  in  the  Past  Three 
Years 

In  comparing  the  two  pictures  it  is  not 
likely  that  the  reader  will  obtain  a 
ratio  of  seven  to  one.  There  is  no 
way  for  the  reader  to  tell  on  what  basis 
the  drawing  was  prepared,  whether  by 
height,  area  or  volume.  The  title  of 
this  chart  is  also  poor  in  that  it  does 
not  name  the  two  years  for  which  the 
comparison  is  made 


22 


GRAPHIC    METHODS 


United  St«te» 

India 

1), 483,000  Bales  of  500  lb 

3,082.000 

Egypt       Russia 

1,506.000 

900.000 

B 

China,  775,000 

Brazil  810,000 

Tarr  and  McMurray's  New  Geographies 

Fig.  19.     The  Six  Leading  Cotton-producing  Coun- 
tries in  1910 

This  arrangement  is  a  bad  one  to  place  before  school  children. 
The  eye  cannot  fit  one  square  into  another  on  au  area  basis  so 
as  to  get  the  correct  ratio 


relative  importance  of  the  materials  listed.  It  frequently  happens  that 
the  second  or  third  item  on  a  list  may  have  only  one-tenth  the  impor- 
tance of  the  first  item.  Because  the  three  names  are  given  one  after 
the  other,  the  pupil  is  quite  likely  to  consider  the  three  items  of  equal 

importance,  just  as  three 
persons  may  be  of  differ- 
ent height,  yet  of  about 
the  same  importance. 
The  graphic  method  judi- 
ciously applied  to  school 
geography  and  to  general 
commercial  geography 
would  make  a  tremen- 
dous difference  in  the 
student's  grasp  of  the 
subject. 

Fig.  19  is  a  typical  example  taken  from  a  geography  book  in  which 
the  attempt  was  made  to  use  the  graphic  method.  The  introduction 
of  the  picture  of  the  bale  of  cotton  in  Fig.  19  is  justifiable.  There  is, 
however,  no  justification  for  placing  the  picture  inside  of  one  of  the  series 
of  squares.  The  picture  detracts  from  the  size  of  the  square.  Graphic 
comparisons,  wherever  possible,  should  be  made  in  one  dimension 
only.     In  such  a  case  as  this,  one-dimension  presentation  is  perfectly 

feasible  by  the  use  of  bars 
of  different  lengths.  The 
pupil  would  find  it  an  al- 
most hopeless  task  to  fit 
one  side  of  the  block  for 
Brazil  into  one  side  of  the 
block  for  the  United  States 
and  then  square  the  result- 
ing ratio  in  order  to  learn 
that  the  United  States  pro- 
duces, roughly,  thirty  times 
as  much   cotton  as  Brazil. 


ssoo 


Tfte  World... — 

United  States ....... . 

India. ^ 

Effypt , 

China 

Asiatic  J?uss'ta 


jooo- 


7500 


The  world's  produc- 
tion of  cotton,  in  ipoj,  in 
millions  of  pounds. 

Dodge's  Advanced  Geography 

Fig.  20.    The  World's  Production  of  Cotton  in  1905 
in  Millions  of  Pounds 

The  above  illustration  together  with  the  title  is  shown  exactly 
as  given  in  a  recent  geography  book.  Charts  like  this 
greatly  assist  the  pupil  in  getting  the  correct  relative  im- 
portance of  the  different  things  studied.  Note  the  scale 
at  the  top  of  the  chart 


Bars  in  one  dimension  only  would  show  the  comparison  accurately. 
Under  any  circumstances,  the  use  of  the  squares  of  Fig.  19  with  the 
center  line  through  the  centers  of  the  squares  gives  an  extremely  poor 
arrangement. 


SIMPLE    COMPARISONS 


23 


VALTTE  OF  PBODTTCTS  FOK  PRINCIPAL  CnTES:  1909. 


ciTies 

NEW  YORK 

CHICAGO 

PHILADELPHIA 

ST.  LOUIS 

CLEVELAND 

OCTflOIT 

PITTSBURG 

BOSTON 

BUFFALO 

(MILWAUKEe 

NEWARK 

CINCINNATI 

BALTIMORE 

MINNEAPOLIS 

tlANSAS  CITY,  KANS. 

SAN   FRANCISCO 

JERSEY  CITY 

INOIANAPOLC 

PROVIDENCE 

ROCHESTER 

LOUISVILLE 

SOUTH  OMAHA 

VOUNOSTOWN 

LAWRENCE 

NEW  ORLEANS 

WORCESTER 

BAYONNE 

AKRON 

PERTH  AMBOY 

LYNN 

PATERSON 

LOS  ANGELES 

BRIDGEPORT 

FALL  RIVER 

PEORIA 

TOLEDO 

OMAHA 

DAYTON 

LOWELL 

VONKERS 

ST.  PAUL 

KANSAS  C'TY.  MO. 

NEW  BEDFORD 

DENVER 

READING 

NEW  HAVEN 

SEATTLe 

WATERBURV 


HUNDREDS  OF  MILLIONS 


1 


Fig.  21.    Value  of  Manufactured  Products  of  Principal  Cities  of  the  United  States 

in  1909 

This  chart,  taken  from  a  Census  office  report,  would  have  been  greatly  improved  if  the  actual  figures  had 
been  placed  at  the  left  of  the  bars  in  the  manner  shown  in  Fig.  27 

It  is  stated  by  the  author  of  the  book  in  which  Fig.  19  is  used 
that  tests  have  shown  that  children  grasp  relative  quantities  better 
when  separate  squares  are  used  than  when  the  information  is  shown 
by  lines  or  bars.  If  this  is  the  case,  it  is  probably  due  to  the  fact 
that  the  squares  appear  more  prominently  to  the  eye  than  do  the  bars, 
and  it  would  seem  that  the  best  kind  of  presentation  might  be  made 
by  using  much  wider  bars  so  that  the  bars  would  be  easily  seen.  Bars 
can  be  made  as  wide  as  some  of  the  squares  seen  in  Fig.  19  and,  if  it 
seems  best,  the  bars  could  be  made  in  outline  rather  than  in  solid 


24 


GRAPHIC    METHODS 


IS  NEWBURGH  SATISFIED  WmilHIS 
SNAU  SCHOOL  EXPENDITURE? 


SCHOOL  COST  PER  PUPIL 


NewIbclEllel 
MLVlErnon  I 
Auburn  I 


{■•^6  7$ 


1  •54-.87 


ilmficrdvnl 
cUmcstinf  n  I 
Newbui^  I 
Waterloiml 


•4-0.27 


■  •36.1S 
»35.+l 


■1  >3^.8& 
'30.2Z 


Cities  25000  to  35. 000  People 
(figures  based  on  average  daily  attendance) 


black.  Wide  bars  would  give  a  striking  visual  effect  and  yet  they 
would  vary  in  one  dimension  only,  so  that  relative  proportions  could 
be  easily  judged.  Wide  bars  would  probably  have  all  the  advantages 
and  none  of  the  disadvantages  of  the  methods  of  either  Fig.  19  or 
Fig.  20.  Instead  of  showing  the  data  of  Fig.  19  by  either  bars  or 
squares,  another  method  would  show  pictures  of  bales  in  rows  of  dif- 
ferent lengths,  on  the  general  scheme  of  Fig.  41.  The  rows  would  be 
the  same  as  the  broad  horizontal  bars,  but  their  numerical  interpreta- 
tion would   be  less  abstract. 

Fig.  20  gives  a  diagram  taken 
from  another  geography  book. 
This  is  a  much  better  form  of 
presentation  than  used  in  Fig.  19. 
It  could,  however,  be  improved  by 
giving  the  figures  for  each  country 
in  connection  with  its  own  bar. 

Fig.  21  shows  the  horizontal- 
bar  method  applied  to  a  larger 
number  of  items  and  proves  the 
great  utility  of  this  method  when 
several  different  items  must  be 
shown  in  their  proper  rank.  In 
this  case,  however,  the  figures 
should  have  been  given  for  the 
convenient  use  of  any  one  who 
might  wish  to  make  ratios  or  to 
quote  the  actual  value  of  products 

for  any  one  of  the  cities.  It  is  exasperating  to  run  across  a  diagram 
of  this  kind  which  contains  valuable  information  in  such  form  that 
it  cannot  be  carried  away  or  quoted  for  use  elsewhere. 

In  Fig.  22  an  attempt  has  been  made  to  show  in  the  graphic 
presentation  the  figures  from  which  each  horizontal  bar  was  drawn. 
The  method  of  placing  the  figures  at  the  right  of  the  bar  is,  however, 
unsafe.  The  eye  is  likely  to  make  a  comparison,  not  from  the  ends 
of  the  bars  themselves,  but  from  the  right-hand  end  of  the  figures- 
Since  the  figures  are  of  about  constant  length,  visual  ratios  are  in- 
accurate when  made  by  comparing  a  short  bar  plus  the  constant^ 
length  of  figures  with  a  long  bar  plus  the  constant  length  of  figures. 
If  the  shortest  bar  in  Fig.  22  were  about  the  same  length  as  the  space 


Department  of  Surveys  and  Exhibits,  Russell  Sage  Foundation 

Fig.  22.  Comparison  of  School  Cost  per 
Pupil  in  Cities  of  25,000  to  35,000 
People  in  New  York  State 

This  illustration  was  photographed  down  from  a 
wall  exhibit  to  adapt  it  to  a  printed  report.  The 
use  of  the  figures  at  the  right-hand  end  of  the 
bars  is  bad  practice.  The  eye  is  apt  to  make 
the  comparison  from  the  last  figures  rather  than 
from  the  ends  of  the  bars 


SIMPLE    COMPARISONS 


25 


UniTea    Kingdom 


JZS7.&,::: 


UniTed    States 

5056  I 

Germany 


required  for  the  figures,  it  would  be  possible  to  make  a  visual  error 
of  100  per  cent  in  the  comparison.  If  the  figures  had  been  placed  at 
the  left  of  the  bars,  they  would  have  been  in  a  neat  column  and  not 

at  all  likely  to  affect  the  ac- 
curacy of  the  visual  com- 
parison. 

The  chart.  Fig.  22,  was 
taken  from  a  report  devoted 
entirely  to  the  city  of  New- 
burgh.  On  this  account, 
it  would  have  been  much 
better  if  the  word  "New- 
burgh"  had  been  printed  in 
heavy -faced  type  so  that  it 
would  stand  out  from  the 
other  cities  in  the  list. 
Where  the  use  of  colored 
ink  is  possible,  it  is  fre- 
quently desirable  to  make 
the  item  under  foremost 
consideration  stand  out 
prominently  by  giving  it  a 
brilliant  color  such  as  red 


Norway 


France 
Br  Colonies 

|i495  i 


Vblues  given  in  Thousands 
of  Tons 


Italy 
Japan 


Netherlands 
{to»|  a 

Fig.  23.    Comparison  of  the  Registered  Shipping 
of  the  Principal  Countries  of  the  World 

The  picture  at  the  top  of  the  chart  assists  in  attracting  the 
attention  of  the  reader.  After  the  attention  is  gained,  the 
bars  set  forth  the  comparison  more  accurately  than  it 
could  be  given  by  any  pictures  of  ships  of  different  sizes  qj.   g-j-egn. 

Fig.  23  is  an  attempt  to  give  a  popular  touch  similar  to  that  at- 
tempted in  Fig.  19  by  the  bale  of  cotton.  As  a  general  thing,  it  is 
possible  to  attract  attention  by  some  such  scheme  as  the  steamship 
used  in  Fig".  23  and  then,  after  the  attention  is  attracted,  to  give  the 
comparison  by  methods  which  are  entirely  correct  and  also  familiar 
to  the  average  observer.  In  Fig.  23  the  figures  are  given  for  the  data 
from  which  the  bars  are  drawn.  The  values,  however,  were  so  large 
that  it  was  necessary  to  leave  off  the  last  three  ciphers  and  state  that 
the  values  given  are  in  "thousands  of  tons."  Though  the  dropping 
of  ciphers  is  very  common,  it  is  a  practice  likely  to  lead  to  serious 
error  and  should  not  be  encouraged.  Even  with  the  ciphers  omitted, 
the  values  could  not  possibly  have  been  given  inside  the  bar  if  more 
countries  had  been  included  in  the  list,  or  if  the  scale  had  been  any 
smaller  than  that  shown  here.  To  place  above  each  bar  the  title  for 
that  bar  is  not  good  practice.     In  general,  it  is  desirable  to  have  a 


26 


GRAPHIC   METHODS 


title  for  each  bar  at  the  left,  then  the  figures,  then  the  bar.  With  such 
an  arrangement,  one  title  will  be  below  another,  easily  perceived  by  the 
eye,  and  the  figures  will  all  be  in  one  column  with  the  decimal  points 

in  a  straight  line.  ^    s^^  ^    un.t£d  states  .  .493  MHHH^HHHHHHl 

Figures    running    h^^^  \     j    mexico  et  ■■ 

y.  ""~/  y    '...  ^       SPAIN&PQRTUGAL  52   HI 

mto  millions  can  be  ^— —^  ^  ""'■^    japan 42  ■§ 

easily  read  from  long  ^  ^    ::3'trau',a:  ■■  Zm  ""**"" "  ^"" 

columns  if  sufficient  ^^§   2^^:;-  :;  II 5 

white  paper  is    left 

between    figures     in  ^^^*  ^^'    Pi"oduction  of  Copper  in  Different  Countries 

me  vertical  arrange-  This  chart  is  a  redrawing  of  Fig.  25.  The  title  here  should  state  the  year, 
ment      and     if      each  ^^^  ^^^^  ^^^  '^^^  given  in  the  book  from  which  Fig.  25  was  taken 

group  of  three  figures  in  the  horizontal  arrangement  is  widely  set  off 
by  means  of  a  comma.  For  graphic  work,  the  groups  of  three  figures 
should,  in  general,  be  more  widely  set  apart  than  they  are  ordinarily. 
Fig.  24  shows  the  arrangement  with  the  figures  at  the  left  of  the 
bars.  Here  again,  however,  the  ciphers  have  been  omitted  when  it 
would  probably  have  been  just  as  clear  if  they  had  been  included  and 
set  off  by  means  of  a  comma  and  a  wide  space.    The  drawing  for  the 

^- y  pigs    of    copper 

e — ^  shown  at  the  left 

\ ->^'^y////  of  the  illustration 

O   '""'^^^^y  gives   an   idea    of 

\   .ZZ///  what  can  be  done 

^  .aA'///////  by  hand  drawing 

\  ZZZ/  in   order  to  at- 

^\  ...f'^^/////       ^g     g  tract  attention  to 

\  ,,,..y///  ^§  ^  §  S  §  §  §  ^^  chart  itself  is 
\.u.^,z^       S     O      3      ^      ^      S      S        intended    to    illu- 

United  States  Mexico      Spain  &      Japan        Chile     Australia  Germany  Canada  .  t  i    • 

Portugal  minate.      in    this 

493,476  61,000        52,188      42.310      42,043        34,339       32.298       28,733  .  , 

PhxHvs'  Chamber  of  Commerce  Atlas  CaSC    thC     lettering 

Fig.  25.    A  Year's  Production  of  Copper  in  Tons  .  also  has  been  done 

This  illustration  was  copied  from  a  prominent  book  on  international  trade.       by    hand    and   is  3, 
Accurate  interpretation  of  the  chart  is  impossible.     Graphic  work  of  _■  1  * 

this  sort  is  dangerous  because  it  may  be  misleading  gOOu     example     OI 

what  a  skilled 
draftsman  may  do  without  any  great  expenditure  of  time.  The  solid 
black  bars  of  Fig.  24  come  out  in  much  better  contrast  than  the  gray 
bars  of  Fig.  23. 


SIMPLE    COMPARISONS 


27 


Federated  Malay 
States 
68,856 


Bolivia 


rig.  25  shows  a  chart  of  the  same  data  from  which  Fig.  24  was 
drawn.  It  is  readily  seen  that  it  would  be  impossible  for  the  average 
reader  to  tell  whether  this  chart  was  drawn  on  the  basis  of  height  or 
the  basis  of  area.  The  pigs  of  copper  are  not  of  the  same  size  in  the 
different  piles,  and  it  is  evident  that  a  pictured  pig  of  copper  is  not 
intended  to  be  the  unit.  If  Fig.  25  is  drawn  on  an  area  basis,  it  is  al- 
most impossible  for  the  eye  to  fit  the  area  for  the  right-hand  pile  into 
the  area  of  the  left-hand  pile.  This  chart  is  a  typical  example  of 
thousands  of  illustrations  used  by  the  popular  magazines  and  even 
by  some  of  the  more  pretentious  reference  books. 

Fig.  26  is  an  even  greater 
atrocity  than  Fig.  25.  In  Fig. 
26,  the  observer  is  entirely  un- 
able to  tell  whether  comparison 
is  made  in  one,  two,  or  three 
dimensions  and  he  has  an  addi- 
tional puzzle  because  of  the  large 
amount  of  perspective  shown 
for  the  top  of  the  pigs  of  tin. 
It  would  be  surprising  if  one  man 
in  a  thousand  could  guess  any- 
thing near  the  ratio  intended  to  be  expressed  between  the  largest  and 
smallest  pigs  shown.  In  general,  graphic  work  of  this  kind  is  much 
worse  than  the  use  of  figures  alone.  There  are  times  when  an  ab- 
sence of  knowledge  is  better  than  incorrect  knowledge. 

Fig.  27  is  a  good  example  of  what  can  be  done  as  a  standard  arrange- 
ment for  simple  comparisons.  On  the  left  there  is  a  symbol  to  attract 
the  eye  and  interest  the  observer. 
Note  that  a  dollar  mark  is  shown 
on  top  of  the  picture  of  the  bale 
of  cotton  in  one  case  and  the  sheaf 
of  wheat  in  the  other,  to  indicate 
that  the  value  of  the  crop  is  con- 
sidered rather  than  the  number  of 
units.  After  the  pictures,  which 
may  be  thought  of  as  "eye  catch- 
ers," we  have  the  figures,  and  then 


Dutch  E.  Austra-  United   Siam 
Indies  lia      Kingdom 

29,937  15,807       12,755     5,052    3,000 

Philips'  Chamber  of  Commerce  Alias 

Fig.  26.  A  Year's  Production  of  Tin  in  Tons 

This  illustration,  taken  from  the  same  source  as  Fig. 
'25,  is  even  more  confusing.  The  perspective  of 
the  tops  of  the  pigs  of  tin  is  such  that  there  is 
no  way  of  telling  whether  visual  comparison 
should  be  made  by  height,  area  or  volume 


COTTON     $  820,320,000 


WHEAT      $561,051,000 


Fig.  27.  Value  of  Cotton  and  of  Wheat 
Produced  in  the  United  States  in  191  o 

Here  is  a  suggestion  for  a  standard  arrangement  for 
horizontal-bar  comparisons.  The  illustrations 
at  the  left  make  the  presentation  popular  in 
form,  yet  actual  figures  for  the  data  are  given 
at  the  left-hand  end  of  the  bars 


the  bars  plotted  to  scale  for  quick  comparison  by  the  reader.    This 
cut  could  have  been  improved  slightly  if  the  spaces  between  the  sep- 


28 


GRAPHIC    METHODS 


arate  groups  of  three  figures  had  been  made  somewhat  larger  and  if 
the  black  bars  had  been  made  about  one  and  one-half  times  as  wide 
as  shown  here. 

TOTAL  POPULATION 


MARRIED 
WIDOWED 
DIVORCED 


SINGLE 
MARRIED 
WIDOWED 
DIVORCED 


SINGLE 
MARRIED 
WIDOWED 
DIVORCED 


NATIVE  WHITE  OF  NATIVE  PARENTS 


SINGLE 
MARRIED 
WIDOWED 
DIVORCED 

^■^ 

^■^ 

^ 

NATIVE  WHITE  OF  FOREIGN  PARENTS 


FOREIGN  WHITE 


NEGRO 


SINGLE 
MARRIED 
WIDOWED 
DIVORCED 


United  states  Statistical  Atlas,  1900  Census 


Fig.  28.     Status  of  the  Population  of  the  United  States  in  1900,  in  Regard  to  Marriage 

This  chart  would  have  been  improved  if  the  figures  had  been  given  at  the  left  and  of  the  bars.    Note  that 
the  four  lower  groups  of  bars  are  a  cross-index  of  the  information  given  in  the  upper  group 

Another  application  of  the  bar  method  is  seen  in  Fig.  28.  Each 
of  the  four  lower  groups  of  population  is  a  subdivision  of  the  total 
population  shown  in  the  upper  group.  The  same  data  may  be 
seen  portrayed  in  a  different  way  in  Fig.  6.  The  arrangement  of 
Fig.  6  is  more  desirable,  in  that  the  size  of  the  components  is  more 
readily  grasped  when  all  are  shown  in  the  same  horizontal  bar.  In 
Fig.  28  the  eye  does  not  readily  make  the  addition  necessary  to  fit 
together  the  four  items  "Single,"  "Married,"  "Widowed,"  and 
"Divorced"  as  percentages  of  the  total  100  per  cent  in  each  group. 

The  drawing  in  Fig.  29  is  a  portion  of  an  illustration  intended 
to  show  how  far  different  kinds  of  trucks  could  travel  for  an  expend- 


SIMPLE    COMPARISONS 


29 


iture  of  one  dollar.  The  placing 
of  these  trucks  on  different  levels 
is  somewhat  confusing,  but  it  was 
done  in  order  that  one  truck  would 
not  have  to  be  shown  back  of  an- 
other. Note  the  bars  behind  each 
truck,  to  give  the  component  parts 
of  the  total  expenditure  split  into 
different  kinds  of  charges.  This 
chart  is  grossly  misleading  because 
the  point  where  the  race  started 
is  not  shown.  It  appears,  for  in- 
stance, that  for  one  dollar  ex- 
pended a  five-ton  gasoline  truck 
will  run  about  twice  as  far  as  a 
five-ton  horse  truck.  This  con- 
clusion is  entirely  unwarranted, 
and  would  not  be  reached  by  any 
reader  if  the  chart  had  been  so 
drawn  that  the  zero  point  or 
starting  point  for  the  race  had 
been  shown  to  scale  at  the  left 
end  of  the  chart. 

The  black  bars  used  in  Fig.  30 
to  show  contagious  diseases  indi- 
cate an  excellent  method  for  differ- 
entiating items  shown  in  graphic 
comparison.  In  the  Boston  health- 
report  illustration  from  which  this 
cut  was  adapted,  the  infectious 
diseases  were  shown  in  red.  By 
making  most  of  the  bars  in  outline 
only,  it  was  possible  in  Fig.  30  to 
use  solid  black  to  get  the  contrast 
obtained  in  the  original  report  by 
means  of  red  ink. 

It  is  frequently  necessary  to 
show  increases  and  decreases  on 
the  same  chart  so  that  they  may 


30 


GRAPHIC    METHODS 


^^        Defttha  from  Infectious  Dlseaacs. 
'       '       De«tbi  from  other  DitemtcB. 

Annual  Report  of  the  Health  Department,  City  of  Boston,  1910 

Fig.  30.  Comparative  View  of  Twenty- 
five  of  the  Principal  Causes  of  Death 
in  Boston  During  1910 

In  the  Boston  report,  the  infectious  diseases  were 
represented  by  red  bars.  Here  attention  is  called 
to  the  infectious  diseases  by  using  solid  black 
bars  in  contrast  with  bars  shown  only  in  outline 

zero  line.  The  figures  can  be 
placed  on  the  left-hand  margin 
of  the  chart,  immediately  between 
the  title  for  each  bar  and  the  end 
of  the  bar,  in  a  manner  similar  to 
that  shown  in  Fig.  27.  Since  the 
zero  line  must  be  near  the  center 
of  the  chart,  rather  than  at  the 
left-hand  edge,  when  the  right- 
and-left  arrangement   is   used,    it 


be  in  contrast.  In  Fig.  31  an  ex- 
ample of  the  contrast  of  increases 
and  decreases  is  given,  increases  be- 
ing shown  to  the  right  of  the  zero 
line  and  decreases  shown  to  the  left 
of  the  zero  line.  This  right-and- 
left  arrangement  of  increases  and 
decreases  is  fairly  well  known  and 
is  so  convenient  that  it  should  be 
more  widely  used.  The  actual 
figures  from  which  each  of  the  hori- 
zontal bars  is  drawn  can  be  shown 
on  the  chart  even  if  the  horizontal 
bars  are  drawn  to  the  left  of  the 

REPfllRdflm  REh^W/lLS  OF  L0C0/10TIVES 

PER  TOn  TRACWE  rORCZ. 
Average  of  6  Year^  Ending  /9/0  Compared       A 

uiih  4-  Kears  Ending  /905.  " 


20         /S        X)         S 


PfMAM 

/rrcf/fE 

LV. 

cn&STp. 

CJf/.&R 

CJ-/YW. 

CJ-A. 

CBiQ.. 

flXJhSE 


0       s      JO       /f      ze      If 

mrEmmoj. 


WESTERnROmS. 


fS      ZO      zs 

"Railroad  Operating  Costs,"  Suffern  &  Son,  Nete  York 

Fig.  31.  Increase  is  Here  Shown  to  the 
Right  of  the  Zero  Line  and  Decrease  to 
the  Left  of  the  Zero  Line.  A  Heavier 
Zero  Line  and  Arrows  Pointing  Right 
and  Left  from  it  Would  Improve  This 
Chart 


SIMPLE    COMPARISONS 


SI 


would  be  well  to  have  a  broad  line  for  the  zero  line,  so  that  the 
eye  may  at  once  perceive  that  zero  is  not  at  the  left-hand  edge  of  the 
chart.  It  would  have  been  better  if  the  zero  line  in  Fig.  31  were  some- 
what broader.  Another  help  to  the  reader  could  be  given  by  placing 
an  arrow  pointing  to  the  right  with  the  word  "increase"  and  an  ar- 
row pointing  to  the  left  with  the  word  "decrease." 


Transformers 

Transmission  Line 

Transformers 

Ifotary  Ccnveitcrs 
Contact  Line 


SINGLE 
PHASE 


SINGLE 
PHASE 

WITHOUT 

Tn*NSFORMERS 


Power  Delivered 
to  Locomotives 


Journal  Amer.  Soc.  Mechanical  Engineers 


Fig.  32.    Comparative  Losses  Between  the  Power  House  and  Locomotives  with  Differ- 
ent Systems  of  Electric  Traction 

The  comparison  of  the  losses  in  the  different  power  systems  is  very  clearly  shown  in  this  illustration,  which 
was  taken  from  a  paper  by  George  Westinghouse 

Broad  bars  can  be  used  either  vertically  or  horizontally.  The  hori- 
zontal arrangement  is  usually  the  more  convenient,  as  it  lends  itself 
more  readily  to  the  use  of  type  and  horizontal  lettering  for  the  titles, 
data,  etc.,  of  each  bar,  without  forcing  the  reader  to  turn  the  book 
at  right  angles.  In  Fig.  S2,  however,  the  lettering  can  perhaps  be 
more  conveniently  grasped  by  the  reader  with  the  bars  placed  ver- 
tically instead  of  horizontally. 

Note  the  lines  connecting  different  bars  to  show  how  the  com- 
ponents compare  in  size  therein.  These  lines  assist  greatly  in  giving 
a  clear  and  rapid  interpretation  of  the  chart. 

Fig.  33  is  an  admirable  example  of  what  the  graphic  method  can 
do  to  boil  down  complex  facts  for  quick  interpretation  by  the  reader. 
In  this  case  the  schools  of  each  of  the  forty -eight  United  States  were 


TEN    TESTS    OF    EFFICIENCY 


f.  WASHINGTON 
2.  MA65ACHU5ETT6 

3  NEW  NORK 

4  CALIFORNIA 

5  COWNECnCUT 
b  OHtO 

7  NLW  JERSEY 

8  ILLINOIS 

9  COLOFJADO 
(0  INDIANA 

1 1  RHODt  I5LAN0 
.12  VERMONT 

\5  UIW  t-IAMRSHIRE 

14  UTAH 

15  OREGON 

16  MONTANA 

17  MICHIGAN 

18  N  DAKOTA 

19  IDAHO 

20  MINNESOTA 

21  IOWA 

22  MAINE 

d5  PENNSYLVANIA 
tA  KAN6A5 

£5  NEBRASKA 
26  5.  DAKOTA 
i7  NLVADA 

26  Wisconsin 

£9  WYOMING 

30  ARIZONA 

31  OKLAHOMA 

32  MISSOURI 

33  W.  VIRGINIA 
54  FLORIDA 

35  DELAWARE 

36  MARYLAND 

37  TEIMNEvSSEE 
58  TEXAS 

39  LOUISIANA 

40  NEW  MEXICO 

41  VIRGINIA 

42  KEKTTUCKY 

43  ARKANSAS 

44  GEORGIA 

45  M1^5»^\PP> 
iJ6  N.  CAROLINA 

47  6.  CAROL\NA 

48  ALABAMA 


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Fig.  33.  Rank  of  States  in  Each  of  Ten  Educational  Features,  1910.  White  Indicates 
that  the  State  Ranks  in  the  Highest  12  of  the  48,  Light  Shading  that  it  Ranks 
in  Second  12,  Dark  Shading  that  it  Ranks  in  Third  12,  and  Black  that  it  Ranks  in 
Lowest  12 

The  above  illustration  is  a  photograph  of  one  page  of  a  pamphlet  issued  by  the  Division  of  Education  of 
the  Russell  Sage  Foundation,  regarding  the  public  schools  of  the  United  States.  This  type  of  chart  i? 
capable  of  wide  application  in  other  fields 

32 


SIMPLE    COMPARISONS 


33 


ADMINISTRATION 


ADMINISTRATION 


MAIL^.'RECORD 


CORRE5P0ND[NC[ 


tNU5T[D  MEN'S 


considered  from  each  of  ten  different  view  points.  The  different 
States  were  then  arranged  in  grades  one,  two,  three,  or  four,  according 
to  the  efficiency  of  their  schools  from  each  of  the  ten  different  points 
of  view  from  which  they  were  considered.  The  best  grade  under 
each  heading  is  shown  by  means  of  a  white  rectangle,  the  second  grade 
by  light  cross-hatching,  the 
third  grade  by  dark  cross- 
hatching,  and  the  fourth 
and  worst  by  solid  black. 
States  are  shown  in  the 
complete  chart  in  their  com- 
parative rank.  The  State 
with  the  best  schools  is 
shown  at  the  top  of  the 
chart  and  the  State  with 
the  worst  schools  is  shown 
at  the  bottom  of  the  chart. 
On  the  chart  as  a  whole, 
one  can  see  at  a  glance  just 
how  the  schools  of  any  State 
rank  with  those  in  the 
other  States,  and  wherein 
the  greatest  defects  occur. 
The  chart  of  Fig.  33  was 
in  a  thirty-page  illustrated 
pamphlet  sent  broadcast 
over  the  United  States  by 
the  Russell  Sage  Founda- 
tion to  members  of  various 
legislatures,  school  boards. 


0FriCER5 


mmiM  RECORD 


ARCHIVES 


CARDING 


S[VENT[ENTH5T. 


J 


Fig.  34.  Organization  of  the  United  States 
Adjutant  General's  Office  Compared  with 
Organization  Proposed  by  President  Taft's 
Commission  on  Economy  and  Efficiency 

This  method  of  connecting  blocks  with  lines  to  show  the  dis- 
position of  departments  can  be  used  in  many  types  of 
chart  presentation 


etc.  This  pamphlet  has 
resulted  in  the  appropriation  of  some  millions  of  dollars  for  the 
improvement  of  public  schools.  The  arrangement  -of  the  pamphlet 
itself  is  worthy  of  note  in  that  each  left-hand  page  is  a  chart,  while 
each  right-hand  page,  facing  the  chart,  is  devoted  to  a  brief  explana- 
tion of  the  conclusions  which  can  be  made  from  a  study  of  the  chart. 
This  arrangement  of  alternate  pages  of  chart  matter  and  printed  matter 
is  tremendously  effective  and  is  well  worth  copying. 

It  is  frequently  necessary  to  contrast  one  grouping  of  components 


I 


34 


GRAPHIC    METHODS 


with  another  grouping  of  components.  In  Fig.  34  we  have  a  chart 
which  may  give  a  valuable  suggestion  to  anyone  who  is  considering 
the  rearrangement  of  departments  in  any  large  organization.  The 
present  arrangement  and  the  proposed  arrangement  are  each  clearly 
indicated,  with  connecting  hues  to  show  instantly  the  disposition  of 
each  of  the  old  departments. 


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N.il.'sliiiii'. 

Writes  riir'.l. 
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1  CVii  lieliver-'. 
.')(3llSi»Iii". 

Fig.  35.  Routing  of  a  Letter  Tiirough  the  Adjutant 
General's  Office  Requesting  the  Discharge  from  the 
Army  of  an  Enlisted  Man  in  Recruiting  Service, 
Contrasted  with  the  Routing  Proposed  by  President 
Taft's  Commission  on  Economy  and  Efficiency 

By  referring  to  the  horizontal  scale  and  to  the  vertical  scale  the  steps 
can  be  studied  either  by  departments  or  by  operations 

In  Fig.  35  is  given  a  convenient  method  to  show  the  routing  of 
papers  through  a  large  office,  together  with  the  operations  through 
which  these  papers  must  pass.  Across  the  top  of  the  chart  is  a  scale 
of  departments.     The  circles  drawn  immediately  below  the  space  for 


SIMPLE    COMPARISONS  35 

any  department  on  the  upper  scale  show  that  the  papers  receive  some 
action  in  that  particular  department.  At  the  right  is  a  scale  showing 
the  nature  of  the  work  done  in  each  of  the  departments.  The  chart 
is  drawn  on  the  basis  of  the  intersection  of  vertical  lines  downward 
from  the  names  of  departments  and  horizontal  lines  through  the 
names  of  the  operations  given  at  the  right.  Arrows  joining  the  various 
circles  then  give  the  routing  of  the  papers  through  the  whole  of  the 
journey.  The  comparison  of  the  existing  routine  with  the  proposed 
routine  can  be  seen  by  considering  the  solid  lines  and  the  dotted  lines 
and  by  comparing  the  two  distinct  columns  or  lists  at  the  right.  Thirty- 
nine  operations  may  be  counted  in  the  present  arrangement  against 
five  operations  in  the  proposed  arrangement.  Though  the  drafting 
and  the  detail  arrangement  of  this  chart  could  be  improved,  the  gen= 
eral  scheme  is  nevertheless  worthy  of  attention. 


Chapter  III 


SIMPLE  COMPARISONS  INVOLVING  TIME 


THOUGH  in  making  comparisons,  the  horizontal  bar  divided  into 
blocks  is  superior  to  the  circle  divided  into  sectors,  the  circle 
and  sector  arrangement  is  not  inaccurate  when  only  the  com- 
ponent parts  of  any  unit  are  to  be  shown.  In  the  case  of  Fig.  36,  how- 
ever, the  comparison  is  between  two  circles,  the  divisions  into  com- 
ponent sectors  being  only  an  incidental 
feature.  In  this  diagram,  copied  direct  from 
the  Statistical  Atlas  of  the  1900  Census,  it 
is  practically  impossible  to  tell  how  much 
larger  the  foreign-born  population  was  in 
1900  than  it  was  in   1850,  ^^^^ 

for  it  is  necessary  to  com- 
pare the  two  circles  on  an 
area  basis.  To  the  average 
person  this  is  an  almost 
impossible  task,  because  it 
is  not  feasible  to  fit  one 
circle  inside  of  the  other 
visually  as  two  horizontal 
bars  may  be  fitted.  If  the 
circle  for  1900  were  esti- 
mated as  twice  the  diameter 
of  the  circle  for  1850,  it 
would  mean  that  the  for- 
eign-born population  in 
1900  was  four  times  as  great 
as  that  in  1850.  If,  how- 
ever, the  ratio  were  some- 
thing less  simple  than  this, 

interpretation  of  the  chart  would  be  difficult  even  by  the  processes 
of    mental    arithmetic.     If  the   ratio    between   the    diameters    were, 

36 


S.^X^  Germans 
F>.3>^  British 
r.W'AW'xN  Canadians 


P^^C^  Scandinavians 
g>:^g<>1  Slavs 
l\\\?V\\1  Italians 
K^y::'^  All  Others 

United  States  Statistical  Atlas,  Census  of  1900 

Fig.  36.  Foreign-bom  Population  of  the  United 
States  in  1850  Compared  with  that  in  1900, 
also  the  Proportion  of  the  Different  Nation- 
alities in  the  Two  Years  Compared 

The  method  of  presentation  by  means  of  a  circle  with  sectors 
is  not  inaccurate  when  only  component  parts  are  to  be 
shown.  Here,  however,  we  have  two  different  circles  com- 
pared on  the  basis  of  total  area.  The  reader  cannot  com- 
pare the  areas  visually  so  as  to  get  the  correct  ratio  meas- 
ure of  the  increase  in  total  number  of  foreign-born  popula- 
tion. Horizontal  bars  are  much  preferable  to  circles  when 
comparisons  are  to  be  made 


COMPARISONS   INVOLVING   TIME 


37 


1910 


1900 


1890 


for  example,  one  and  a  half,  the  average  reader  would  be  completely 
nonplussed,  as  he  would  not  trouble  to  go  through  the  mental  arith- 
metic of  multiplying  one  and  a  half  by  one  and  a  half.     In  general,  the 

comparison  of  two  circles 
of  different  size  should 
be  strictly  avoided. 

Many  excellent  works 
on  statistics  approve  the 
comparison  of  circles  of 
different  size,  and  state 
that  the  circles  should 
always  be  drawn  to  rep- 
resent the  facts  on  an 
area  basis  rather  than  on 
a  diameter  basis.  The 
rule,  however,  is  not  al- 
ways followed  and  the 
reader  has  no  way  of  telling  whether  the  circles  compared  have  been 
drawn  on  a  diameter  basis  or  on  an  area  basis,  unless  the  actual 
figures  for  the  data  are  given  so  that  the  dimensions  may  be  verified. 


1.647  2,244  3.302 

Figures  in  Millions  of  Dollars 

Fig.  37-  Total  Yearly  Value  for  the  United  States 
of  Combined  Imports  and  Exports  by  Land  and 
by  Sea 

In  this  illustration  the  data  have  been  represented  by  circles 
drawn  on  a  diameter  basis.  The  right-hand  circle  appears 
more  prominent  than  the  data  would  justify.  Circles  com- 
pared on  a  diameter  basis  mislead  the  reader  by  causing  him 
to  over-estimate  the  ratios.     Compare  Fig.  38 


In  Fig.  37  the  figures 
are  given,  and  the  circles 
have  been  drawn  on  a 
diameter  basis.  It  will  be 
noted  that  the  figures  for 
1910  are  roughly  twice 
those  for  1890.  The  circle, 
however,  has  roughly  four 
times  the  area  of  the  circle 
for  1890  and,  according- 
ly, seems  to  have  much 
more  thafl  twice  the  im- 
portance. In  Fig.  38,  the 
same  data  have  been 
shown  on  an  area  basis 


1890 


1900 


1910 


1.647  2.244  3,302 

Figures  in  Millions  of  Dollars 

Fig.  38.  Total  Yearly  Value  for  the  United  States 
of  Combined  Imports  and  Exports  by  Land 
and  by  Sea 

Here  the  data  of  Fig.  37  have  been  shown  by  means  of  circles 
drawn  on  an  area  basis,  as  recommended  by  many  authorities 
on  statistical  work.  The  right-hand  circle,  however,  shows  up 
less  prominently  than  the  figures  would  justify.  Circles  com- 
pared on  an  area  basis  mislead  the  reader  by  causing  him  to 
underestimate  the  ratios.  Circles  of  different  size  should  never 
be  compared.  Horizontal  bars  have  all  the  advantages  of 
circles  with  none  of  the  disadvantages 


as  most  of  the  authorities  on  statistical 
work  recommend.  If  the  figures  were  not  given,  the  reader  would  be 
forced  to  fit  the  left-hand  circle  into  the  right-hand  circle  on  an  area 
basis,  or  else  make  a  ratio  between  the  diameters  and  then  square  the 
ratio.    Either  process  is  almost  impossible  to  accomplish  and  there  is 


38 


GRAPHIC    METHODS 


o 
o 

I 

\0 
G) 


MINISTRY 


LAW         MEDICINE     EDUCATION  BUSINESS     PUBLIC  SERVICE 


o 
o 

2 
T 
vo 

0) 
00 


MINISTRY 


LAW 


MEDICINE      EDUCATION         BUSINESS     PUBLIC  SERVICE 


Independent 

Fig.  39-     Proportion  of  College  Graduates  in  Different  Professions  in  1696-1700  and 

in  I 896- I 900 

Charts  of  this  kind  with  men  represented  in  different  sizes  are  usually  so  drawn  that  the  data  are  represented 
by  the  height  of  the  man.  Such  charts  are  misleading  because  the  area  of  the  pictured  man  increases  more 
rapidly  than  his  height.  Considering  the  years  1690-1700,  the  pictured  minister  has  about  two  and  one- 
half  times  the  height  of  the  man  representing  public  service.  The  minister  looks  over-important  because 
he  has  an  area  of  more  than  six  times  that  of  the  man  drawn  to  represent  public  service.  This  kind  of 
graphic  work  has  little  real  value 

no  necessity  of  inflicting  such  cruelty  on  a  reader.  Though  the  circles 
in  Fig.  37,  drawn  on  a  diameter  basis,  exaggerate  the  ratios,  the  circles 
in  Fig.  38,  plotted  on  an  area  basis,  make  the  reader  underestimate 
the  ratio.  Comparison  between  circles  of  different  size  should  be 
absolutely  avoided.  It  is  inexcusable  when  we  have  available  simple 
methods  of  charting  so  good  and  so  convenient  from  every  point  of 
view  as  the  horizontal  bar. 

In  Fig.  37  and  in  Fig.  38,  it  would  have  been  better  if  the  year 
had  been  given  under  each  circle,  with  the  figures  for  quantity  placed 
above  the  circles,  so  as  to  follow  the  standard  arrangement  of  having 


COMPARISONS    INVOLVING    TIME 


39 


1911 


1899 


14.591.000 
One  Mile 


32.837,000 
One  Mile 


dates  placed  always  at  the  base  of 
the  chart. 

Another  difficulty  in  the  com- 
parison of  areas  is  shown  in  Fig. 
39.  No  figures  have  been  given 
and  the  helpless  reader  must  com- 
pare by  means  of  the  pictures 
alone.  By  measurement,  it  will  be 
seen  that  the  minister  in  1700  has 
over  three  times  the  height  of  the 
minister  in  1900.  Since  the  man 
in  each  case  is  shown  in  his  natural 
proportions,  the  picture  of  the 
minister  in  1700  has  over  nine 
times  the  area  of  the  picture  for 
1900.  Whether  the  ratio  should 
be  roughly  three  or  roughly  nine, 
we  cannot  tell. 

Another  example  of  the  same 
kind  of  difficulty  appears  in  Fig.  40, 
but  here  the  figures  are  given  and 
we  can  check  up  the  author  to  see 
whether  he  has  drawn  the  1911  man  on  the  basis  of  height  or  on  the 
basis  of  area.  The  1911  man,  on  account  of  his  far  greater  area,  looks 
to  be  rather  more  than  two  and  a  quarter  times  as  important  as  the 
man  of  1899.  Though  this  type  of  graphic  work  is  quite  common,  it 
should  be  avoided,  for  its  visual  inaccuracy  is  serious  enough  to  cause 
distrust  of  the  whole  graphic  method.    In  considering  Fig.  40,  the  point 


World's  Work 

Fig.  40.  Passengers  Carried  on  the  Rail- 
roads of  the  United  States  in  1899 
and  in  191 1  Compared 

This  illustration  has  all  the  bad  features  mentioned 
for  Fig.  39.  Here  the  numerical  data  are  given 
and  we  can  prove  for  ourselves  that  the  two 
pictured  men  are  compared  on  the  basis  of 
height.  Because  of  the  disproportionate  area, 
the  right-hand  picture  gives  the  reader  a  false 
and  exaggerated  impression  of  growth.  See 
Fig.  41 


1899 


14,591,000 
ONE  MILE 


1911    32.837000 
'    "   ONE  MILE 


Fig.  41.    Number  of  Passengers  Carried  on  the  Raikoads  of  the  United  States  in  1899 

and  in  191 1  Compared 

Here  is  a  chart  drawn  from  the  same  data  as  Fig.  40.  It  was  not  a  larger  passenger,  but  more  passengers, 
that  the  railroads  carried.  The  ratio  expressing  increase  in  business  can  be  clearly  and  accurately  seen 
from  this  method  of  portraying  the  facts 


40 


GRAPHIC    METHODS 


123.667,000.000  Tons 


1911 


250.440.000.000  Tons 


World's  Work 

Fig.  42.     Comparison  of  the  Total  Amount  of  Freight  Service  on  the  Raihoads  of 
the  United  States  in  1899  and  in  191 1 

It  would  have  improved  this  illustration  if  the  two  locomotives  had  been  shown  one  exactly  above  the  other 
facing  to  the  left.  The  additional  cars  representing  the  increase  in  1911  would  then  be  seen  as  though 
added  to  the  rear  of  the  train 


to  be  brought  out  is  not  that  the  railroads  carried  a  larger  passenger 
in  1911,  but  that  they  carried  more  passengers. 

If  it  is  necessary  to  have  a  popular  method,  we  can  at  least  be 
accurate  by  portraying  the  data  in  the  form  of  Fig.  41,  not  as  in  Fig. 
40.  Copy  for  an  illustration  of  this  sort  is  very  simply  made  by  taking 
proofs  from  a  cut  of  one  man  and  then  pasting  these  proofs  on  a  long 
strip  of  paper  until  a  row  of  the  correct  length  is  obtained.  The  whole 
arrangement  can  then  be  photographed  down  to  produce  the  effect 
shown  in  Fig.  41.  To  avoid  fractional  men  at  the  end  of  a  row,  it  is 
usually  easy  to  express  the  ratio  with  a  sufficient  number  of  men  in 
each  row  or  bar  to  get  numerical  correctness.  Note  that  in  Fig.  41 
the  whole  arrangement  is  similar  to  that  of  Fig.  24  or  Fig.  27  in  Chapter 
II,  the  actual  data  being  given  at  the  left  of  the  row  or  bar.  It  would 
have  been  better  if  the  men  in  Fig.  41  had  been  faced  to  the  left  in- 
stead of  to  the  right.  The  additional  men  in  the  row  for  1911  would 
then  appear  to  have  joined  the  rear  of  the  line  rather  than  to  have  come 
in  at  the  front  of  the  line. 

1901 


xox 


TTTT 


Ddncf^ 


1912 


3X3X: 


'rrrv  rrn^%FOr>— ri-R^ 


World's  Work 

Fig.  43.     Comparison  in  Size  of  Trainload  on  the  Chicago,  BurUngton  &  Quincy  Rail- 
road in  1901  and  in  191 2 

Here  one  locomotive  is  above  the  other  but  both  face  in  the  wrong  direction.  Figures  for  the  data  are  not 
given  and  the  reader  cannot  tell  whether  the  two  lengths  compared  should  include  the  locomotives  or 
only  the  cars.  Clearness  could  have  been  assured  if  the  cars  had  been  shown  for  comparison  in  solid 
black,  with  the  locomotives  included  for  pictorial  effect,  but  only  in  outline 


COMPARISONS   INVOLVING  TIME 


41 


In  Fig.  42  the  idea  is  brought  out  that  the  railroads  are  now  han- 
dhng  more  freight.  The  drawing,  however,  should  be  reversed  so  as  to 
have  the  two  locomotives  one  above  the  other  facing  to  the  left,  with 
the  additional  cars  at  the  right-hand  end.  It  would  also  be  better 
if  the  dates  for  the  two  years  and  the  figures  representing  tons  had 
been  placed  at  the  extreme  left  in  the  manner  shown  in  Fig.  41. 

In  Fig.  43,  the  two  locomotives  are  placed  neck  and  neck,  but 
the  whole  chart  reads  backwards  in  that  it  reads  to  the  left  instead 
of  to  the  right.  Turn  the  page  over  and  hold  it  up  to  the  light.  Through 
the  back  of  the  paper,  the  arrangement  of  the  cars  appears  from  left 
to  right  as  it  should. 


I870 


leeo 


I890 


1900 


303=100  y. 

20 

227=74  9  V, 


PRODUCTION 
EXPORT 

UPPER  Figures 

MILLIONS    OF   BALES 
LOWER   FIGURES 

MILLIONS   OF   DOLLARS 


9  4 

59 

357  =  100  "4 

1 

241  =  67  S  "/, 

wwsfflffiflHlBBlBtHBBHiti^HflmiflesifiBlHSfBffi 

Fig.  44.  Yearly  Cotton  F*roduction  and  Export  of  the  United  States.  The  Figures 
with  the  Arrows  Show  the  Number  of  Millions  of  Bales  and  also  the  Value  in 
Millions  of  Dollars 

•    If  horizontal  bars  are  used  to  represent  years,  the  earliest  year  should  be  shown  at  the  top  as  seen  here 

No  data  are  .given  in  Fig.  43,  and  it  is  impossible  to  tell  whether 
the  comparison*  between  1901  and  1912  should  be  based  on  the  ratios 
of  the  whole  length,  including  engines,  or  whether  it  should  be  based 
on  the  lengths  for  cars  only.  A  ratio  without  the  engines  would  be 
much  larger  than  with  engines.  This  chart  is  accordingly  unrehable. 
The  difficulty  in  regard  to  engines  being  included  in  the  drawing 
could  be  entirely  overcome  if  the  freight  cars  were  made  in  solid  black, 
with  the  engines  shown  in  outline  only,  so  that  the  eye  could  judge 
the  ratio  between  the  solid  black  bars  representing  freight  cars  without 
including  the  outline  drawings  of  the  engines. 

Often  in  charting  information  like  that  given  in  Fig.  44,  vertical 
bars  instead  of  horizontal  bars  are  used.  However,  the  figures  given 
in  Fig.  44  in  conjunction  with  the  bars  make  it  desirable  that  the  bars 
should  here  be  horizontal  in  order  that  the  figures  may  be  read  easily. 


42 


GRAPHIC    METHODS 


AVERAGE  VALUE  OF  AMERICAN  AUTO  EXPORTS 

1912 

$990 

1911 

$1,100 

1910 

$1,380 

1909 

$1,700 

1908 

$1,880 

THE  RISE  OF  THE  LOW-PRICED  CAR 

SHOWING   HOW   THE  AVERAGE  VALUE   OF   EXPORTED 
AMERICAN       AUTOMOBILES       HAS      DROPPED     IN      FIVE 

YEARS 

World's  Work 

Fig.  45.  The  Illustration  and  the  Titles 
are  Shown  Above  Exactly  as  Origi- 
nally Printed 

The  reader  is  misled  if  he  does  not  notice  that  the 
earliest  year  has  been  shown  at  the  bottom 
instead  of  at  the  top.  The  wording  of  the  two 
titles,  when  taken  in  conjunction  with  the  chart, 
really  adds  to  the  general  confusion 


The  arrangement  of  dimension 
marks  with  an  arrow-head  at  each 
end  is  a  convenient  scheme  worthy 
of  wide  use.  Note  that  the  per- 
centage figures  in  the  illustration 
clearly  refer  to  the  value  of  the 
cotton  rather  than  to  the  number 
of  bales.  The  figures  representing 
time,  in  this  case  years,  read  down- 
ward as  they  should  do  in  every 
case  in  which  horizontal  bars  are 
used  to  represent  facts  at  different 
periods  of  time.  If  the  horizontal 
bars  are  arranged  with  the  earliest 
date  at  the  top,  any  reader  who 
wishes  to  do  so  may  read  the  chart 
as  a  curve  from  the  left-hand  edge 
of  the  page  and  the  dates  will  then  appear  in  correct  order  from  left 
to  right. 

In  Fig.  45  the  latest  date  has  been  placed  at  the  top  of  the  chart. 
This  causes  an  impression  absolutely  the  reverse  of  what  it  was  in- 
tended to  bring  out 
by  the  drawing.  Any 
one  glancing  at  this 
chart  is  likely  to 
suppose  that  the 
earlier  year  is  indi- 
cated at  the  top  and 
probably  would  not 
notice  that  the 
draftsman  in  this 
case,  for  some  unjus- 
tifiable reason,  has 
reversed  the  correct 
arrangement. 

In    Fig.  46  also, 


PASSENGER 

AND   FREIGHT  REVENUES 

(Average  for  U.  S.) 

PER  MILE  OF  ROAD 

Average 

Ratio  of 

Receipts 

Average 

Average 

Averag* 

Operating 

No.  of 

No.  of 

per 

Receipts 

Journey 

-Haul 

Eirpenses  to 

Date 

Net 

Passengers 

Tons 

Passenger 

per  Ton 

per 

per  Ton, 

Operating 

Operating 

Carried 

Carried 

per  Mile, 

per  Mile, 

Passenger, 

Miles. 

Revenues, 

Revenue 

1  Mile 

1  Mile 

Cents 

Cents 

Mifcs 

Per  cent 

1908* 

$3171 

130  073 

974  654 

1.937 

.754 

32.86 

143. 83 

69.75 

m? 

3  696 

123  259 

1  052  119 

2  014 

.759 

31.72 

131.71 

67.53 

1906 

3  548 

114  529 

982  401 

2.003 

.748 

31.54 

132. 33 

66.08 

1905 

3  189 

109  949 

861396 

1.962 

.766 

32.21 

130.60 

65.78 

H()4 

2  998 

104  198 

829  476 

2006 

.780 

30.64 

133.23 

67. 79 

HH 

3  133 

103  291 

855  442 

2  006 

.763 

30.10 

132.80 

66.16 

190;i 

3  048 

99  314 

793  351 

1.986 

.757 

30.30 

131.04 

64.66 

1901 

2  854 

89  721 

760  414 

2.013 

.750 

28.58 

135.03 

64.86 

lyou 

2  729 

83  290 

735  352 

2.003 

.729 

27.80 

130.87 

64.65 

1H9!+ 

2  435 

77  821 

659  565 

1.978 

.724 

27.89 

131. 04 

65.24 

1898 

2  325 

72  462 

617  810 

1.973 

753 

26.70 

132.09 

65.58 

Courtesy  of  "Data,"  Chicago 

Fig.  46.    Average  Railroad  Revenues  from  Passengers  and 
from  Freight  in  the  United  States 

Here  again  the  earliest  year  has  been  shown  at  the  bottom  instead  of  at 
the  top.  In  tabulations  of  this  sort  there  is  less  danger  of  erroneous 
reading  if  the  earliest  year  is  shown  at  the  top.  Years  are  usually 
grouped  in  fives,  including  in  one  group  years  ending  from  one  to 
five  inclusive,  and  in  the  next  group  years  ending  from  six  to  ten 
inclusive 


the  latest  year  has  been  placed  at  the  top  of  the  column  instead  of  at 
the  bottom  of  the  column.  Though  some  precedent  could  probably 
be  found  for  such  an  arrangement,  the  arrangement  nevertheless  seems 


COMPARISONS    INVOLVING    TIME 


43 


VALUE,  AMERICAN  EXPORTS 

1906                    $4,409,136 

1911                    $21,636,661 

1912                   $28,300,139 

VALUE,  IMPORTS  FROM  ABROAD 

1906                     $4,910,208 

1911                      $2,446,248 

1912                     $2,000,000 

an  unfortunate  one  which  should 
not  be  copied.  Note  that  in  Fig.  46 
the  figures  have  been  arranged  in 
groups  of  four  with  a  blank  space 
to  assist  the  eye  in  reading  across 
the  page.  In  general,  it  is  cus- 
tomary to  have  such  figures  not 
in  groups  of  four  but  in  groups  of 
five,  the  groups  including  years 
ending  in  1  to  5  inclusive  and  6  to 
10  inclusive. 

A  rapid  reader  seeing  Fig.  47  is 
likely  to  get  a  much  exaggerated 
idea  of  the  increase  in  the  Amer- 
ican exports  of  automobiles.  The 
arrangement  of  the  three  hori- 
zontal bars  for  the  three  years  is 
such  that  the  reader  is  justified  in 
assuming  that  the  years  are  con- 
secutive. He  is  not  likely  to 
notice  that  the  upper  bar  repre- 
sents the  year  1906  and  that  four 
years  are  omitted  between  1906  and  the  consecutive  years  1911  and 
1912.     Since   there   is   nothing  to  indicate  that  years  have  been  left 

out  after  1906,  the  reader  seeing 


A    MARVEL   OF    EXPORT  TRADE 

SHOWING  THE  AMAZING  INCREASE  IN  OUR  EXPORTS 
OF  MOTOR  CARS,  AND  THE  STEADY  DECREASE  IN  OUR 
IMPORTS,    IN    THE    LAST    SEVEN    YEARS 

World's  Work 

Fig.  47.  This  Illustration  was  Originally 
Printed  with  Fig.  45  on  the  Same 
Page  of  a  Magazine,  yet  in  Fig.  45 
the  Earliest  Year  was  Shown  at  the 
Bottom  While  Here  the  Earliest  Year 
is  Properly  Shown  at  the  Top 

There  is,  however,  danger,  in  this  illustration,  that 
the  reader  may  assume  that  the  three  bars  rep- 
resent consecutive  years  without  noticing  the 
jump  from  1906  to  1911.     Compare  Fig.  48 


Value,  American  Exports 

1906      ^4,409,136    IH 


1911 
1912 


21,636,661 
28,300,139 


Value,  Imports  from  Abroad 


1906 

1911 
1912 


4,910.E08 

2.446,248 
2,000,000 


Fig.  48.     The  Contrast  of  American  Ex- 
ports and  Imports  of  Automobiles 

The  data  of  Fig.  47  have  here  been  redrawn.  The 
values  have  been  shown  at  the  left  of  the  bars, 
where  they  give  the  neatest  and  most  convenient 
arrangement.  Note  that  the  bar  for  1906  is 
somewhat  separated  from  the  bar  for  1911,  so 
as  to  indicate  to  the  reader  that  the  three  bars 
do  not  represent  consecutive  years 


the  figure  1912  is  apt  to  assume 
that  the  two  earher  years  are  1911 
and  1910. 

Fig.  48  is  a  redrawing  of  Fig. 
47  with  a  change  in  scale  to  indi- 
cate to  the  reader  that  the  earher 
year  shown  for  comparison  must 
not  be  read  as  one  of  three  con- 
secutive years.  Though  the  space 
left  between  the  bars  for  1906  and 
1911  would  not  be  sufficient  for 
the  four  omitted  years,  if  the 
whole  chart  were  drawn  to  scale, 
the    space    is    nevertheless    large 


44 


GRAPHIC   METHODS 


enough  to  serve  as  a  safeguard  to  the  reader.  A  slight  break  could 
indicate  in  this  manner  a  gap  of  any  large  number  of  years  which  it 
would  not  be  feasible  to  denote  by  allowing  space  according  to  scale. 
In  Fig.  48  the  years  and  the  figures  for  the  chart  are  properly  shown 
to  the  left  much  as  they  are  shown  in  Fig.  24  and  in  Fig.  27. 


1912 


1911 


BU. 

SB 

BU. 

1912 


1911       1912 


1911       1912 


New  York  Times  Annalist 


Fig.  49.    The  Size  and  the  Value  of  the  Com  Crop  of  the  United  States  in  191 1  Com- 
pared with  that  of  19 12 

The  object  of  the  chart  is  to  show  that,  though  there  were  more  bushels  of  corn  in  1912,  the  producer  re- 
ceived less  total  money  than  in  1911. 

The  left-hand  illustration  is  incorrectly  made  as  it  shows  the  earlier  year  to  the  right.  In  the  central 
illustration  this  error  has  been  corrected  and  the  years  are  named  at  the  base  instead  of  at  the  top. 
The  arrangement  still  fails,  however,  to  bring  out  the  message  clearly. 

From  the  right-hand  presentation  it  can  be  seen  instantly  that  the  number  of  bushels  has  increased  while 
the  total  money  received  has  actually  decreased.  The  right-hand  presentation  is  arranged  in  accord- 
ance with  the  working  of  the  average  person's  mind  and  it  gains  in  clearness  accordingly 

The  left-hand  group  in  Fig.  49  was  used  as  an  illustration  in  a 
business  magazine.  The  purpose  of  the  chart  was  to  show  that  in 
1912  the  farmers  of  the  country  raised  more  bushels  of  corn  than  in 
1911  but  received  less  total  money  in  return.  Note  that  the  earlier 
year  is  placed  at  the  right  instead  of  at  the  left,  and  that  the  dates 
are  given  at  the  top  rather  than  at  the  bottom.  The  middle  group 
of  bars  corrects  the  error,  but  the  information  is  still  not  as  clearly 
brought  out  as  it  should  be.  The  best  way  to  bring  out  this  informa- 
tion is  to  show  that  the  number  of  bushels  has  increased  while  the 
number  of  dollars  has  decreased,  and  this  is  not  clear  from  the  middle 
drawing.  In  the  right-hand  presentation  it  is  clearly  seen  that  the 
bushels  went  up  though  the  total  value  came  down.  The  right-hand 
drawing  follows  the  working  of  the  average  person's  mind  and  it  gains 
in  clearness  accordingly. 

As  a  general  rule  dates  should  always  be  arranged  to  read  from 
left  to  right,  and  columns  of  figures  should  be  arranged  with  the  col- 
umn for  the  earlier  date  at  the  left.  A  common  exception  is  made, 
however,  in  the  case  of  financial  reports  when  it  is  desired  to  show 
the  most  recent  year  next  to  the  various  type-headings  relating  to 


COMPARISONS    INVOLVING    TIME  45 

earnings,  expenses,  etc.,  as  in  Fig.  50.  In  the  case  of  financial  reports 
it  is  always  the  latest  year  which  is  of  chief  interest,  and  for  this  reason 
the  arrangement  of  Fig.  50  seems  permissible  in  order  that  the  figures 
and  the  account  names  may  be  side  by  side.  The  problem  in  Fig.  49 
is  so  entirely  different  from  that  in  Fig.  50,  that  the  method  of  Fig.  50 
cannot  be  held  as  a  precedent  to  justify  the  reversed  arrangement 
of  dates  shown  at  the  left  of  Fig.  49.  The  fact  that  one  needs  an 
umbrella  on  a  rainy  day  is  not  sufficient  reason  for  carrying  an  um- 
brella at  all  times. 

*  •  • 

UNION  BAG  AND  PAPER  COMPANY— Reports  for 
the  year  ended  Jan.  31 : 

1913.          1912.  1911.          1910. 

Net  earnings   $554,251  $1,017,835  $1,038,112  $1,055,400 

Depr.    and   ext.    fd.    122,585       122,205  120,987       149,925 

Balance     431,000       895,570  917,125       905!47o 

Skg.  fd.  &  bd.  red.    134,025       114,095  110,745       107!t5o.j 

Balance     296,741       781,475  806.380       797^870 

Interest     253,748       202,480  197.135       204!61l 

Balance    for    divs..      42,903       578,995  609,245       593,259 

Preferred    dividend    330,<X)0       440,000  440,000       44oioO(> 

Deficit     287,0<)7     •138,995  •109,245     •153,259 

Prev.    surp 1,921,788    2,020,471  1,851,226    1,097,968 

Bond    disc.    &    exp.      70,945       237,677 

Profit  and  loss  sur.l, 563.836    1.921,788  2.020,471    1,851,220 

•  •    • 

New  York  Times  Annalist 

Fig.  50.    Brief  Financial  Statement  Regarding  the 
Union  Bag  and  Paper  Company 

In  condensed  statements  of  this  sort  there  seems  to  be  good 
reason  for  placing  next  to  the  headings  at  the  left  the  column 
of  figures  for  the  latest  fiscal  year,  since  this  information 
is  of  most  vital  interest  to  the  reader.  Columns  for  other 
years  are  then  printed  to  the  right  for  comparative  pur- 
poses.    The  earliest  year  is  shown  at  the  extreme  right 

Though  this  reversed  arrangement  of  years  seems  permissible 
for  the  purpose  of  printed  reports  as  here  used,  there  is 
no  justification  for  the  use  of  the  reversed  arrangement  in 
chart  work.  As  a  general  rule  material  given  by  years 
should  be  shown  with  the  earliest  year  at  the  left 

Fig.  51  is  an  illustration  photographed  down  from  a  large  drawing 
used  in  a  wall  exhibit.  It  is  a  fair  example  showing  what  can  be  done 
to  arouse  interest  by  the  judicious  embellishment  of  charts,  especially 
of  those  for  wall  exhibits  intended  to  reach  a  miscellaneous  audience 
having  an  average  of  rather  limited  education.  Note  the  smoke- 
stacks in  Fig.  51.  The  smoke-stack  at  the  left  is  the  same  height  as 
the  bar  for  the  year  1906-07,  and  the  taller  smoke-stack  at  the  right 
the  same  height  as  the  bar  for  1912-13.  As  this  drawing  was  made 
for  a  wall  exhibit  to  show  the  co-operation  of  manufacturing  companies 
with  the  college,  the  pictorial  embellishment  seems  quite  justifiable 
and  useful  to  attract  attention  to  this  particular  exhibit.    A  pictorial 


46 


GRAPHIC    METHODS 


THE    NUMBER   OF  FIRMS 
CO-OPERATING     WITH    THE 

ENGINEERING      COLLEGE 

OF    THE 

UNIVERSITY    OF    CINCINNATI 

HAS     INCREASED    S8S  >: 


^ 


effect  also  relieves  monotony  in  a  large  exhibition  which  may  have 
hundreds  or  even  thousands  of  different  charts  and  other  wall  exhibits. 
Fig.  52  was  shown  in  conjunction  with  Fig.  51  with  the  idea  of 
pointing  out  that  the  number  of  students  in  the  University  of  Cin- 
cinnati had  increased  just  as  (according  to  Fig.  51)  the  number  of 
firms   co-operating   in   the   engineering   work   of   the  University  had 

increased  in  the  same  time. 
The  bars  in  Fig.  51  and 
Fig.  52  are  placed  vertically, 
each  bar  representing  a  year. 
This  vertical  arrangement  of 
bars  permits  reading  the  chart 
as  if  a  curve  had  been  made 
by  drawing  a  line  through  the 
tops  of  all  the  bars.  Curves 
are  the  common  language  of 
engineers  and  statisticians. 
In  order  that  the  bars  may 
be  read  as  curves,  it  is  desir- 
able to  have  the  bars  placed 
in  a  vertical  position,  if  they 
represent  divisions  of  time, 
rather  than  entirely  distinct 
subjects  such  as  the  separate 
cities  compared  as  to  the 
value  of  their  output  of  manu- 
factured products,  in  the  chart 
reproduced  in  Fig.  21. 
Lettering  like  that  shown  in  Fig.  51  or  Fig.  52  is  conveniently 
made  by  using  the  gummed  black-paper  letters  and  figures  which  can 
be  obtained  in  many  good  stationery  stores.  A  thin  pencil  line  as  a 
guide  at  the  bottom  of  the  letters,  and  some  judgment  used  in  spacing, 
will  assist  greatly  in  getting  a  neat  result  from  the  gummed  letters. 
Large  bars  like  those  shown  in  Fig.  51  and  Fig.  52  can  be  made  by 
cutting  out  strips  of  black  paper  and  pasting  them  onto  white  card- 
board. Such  work,  however,  must  be  very  carefully  done  or  the  bars 
will  curl  on  the  edges  and  give  an  unpleasant  effect.  It  is  generally 
better  to  use  India  ink  in  making  the  bars  if  a  good  result  is  to  be 
assured.     The   liquid   drawing  ink   sold  at  most  stationery  stores  is 


American  licview  of  Reviews 

Fig.  51.  The  Increasing  Number  of  Business 
Firms  Co-operating  with  the  Engineering 
College  of  the  University  of  Cincinnati 

\Mien  the  bars  represent  years  or  other  divisions  of  time, 
a  vertical  arrangement  of  the  bars  is  usually  more 
desirable  than  the  horizontal  arrangement  seen  in  Fig. 
44.  With  the  vertical  arrangement  a  line  may  be 
imagined  joining  the  tops  of  the  bars  so  as  to  give  a 
"curve". 

Note,  in  this  illustration  of  a  wall  chart,  the  popular  touch 
given  by  the  pictures  of  manufacturing  plants  with 
smoke-stacks  of  the  same  height  as  the  first  and  the 
last  vertical  bars 


COMPARISONS    INVOLVING    TIME 


47 


INCREASE   IN  STUDENTS  INl 
CO-OPERATIVE   COURSE 
ENGINEERING    COLLEGE 

INCREASE      1913      OVER    .1907 

12S2 


illll 


available  in  many  different  colors.  Some  grades  of  the  drawing  ink 
are  water-proof  after  drying.  On  elaborate  charts  the  water-proof 
quality  should  always  be  used  to  make  certain  that  a  few  rain  drops, 
or  handling  with  moist  hands,  will  not  ruin  the  finished  work. 

In  the  discussion  of  Fig.  51  and  Fig.  52  it  w^as  mentioned  that  a 
line  could  be  drawn  through  the  tops  of  the  vertical  bars  to  give  a 
curve.  If  the  curve  were  actually  drawn,  the  bars  themselves  would 
be  omitted.  In  Fig.  53,  instead  of  using  bars, 
we  have  lines  which  may  be  considered  as  curves 
for  each  of  the  several  items  compared.  In  this 
case  it  would  be  impossible  to  use  bars  for  each 
of  the  items  shown  because  the  bars  would  cover 
each  other.  The  bars  are  entirely  omitted  and 
lines  are  simply  drawn  from  the  100  per  cent 
point  in  1897  to  the  various  points  for  different 
items  in  1907.  It  is  certain  that  the  prices  (that 
of  pine  lumber,  for  instance,  shown  by  the  upper 
curve)  did  not  have  the  uniform  rate  of  increase 
which  the  straight  line  from  1897  to  1907  would 
indicate.  We  are  considering  here,  however,  the 
changes  over  the  period  as  a  whole,  and  we  can 
for  simplicity  draw  a  straight  line  and  neglect 
all  the  fluctuations  of  intervening  years.  The 
general  scheme  of  Fig.  53  is  convenient,  as  the 
neglect  of  detail  brings  the  main  information  out 
clearly.  Fig.  53  has,  unfortunately,  been  drawn 
in  a  misleading  manner  in  that  the  reader  is 
likely  to  interpret  the  curves  as  if  zero  were 
show^n  at  the  bottom  of  the  chart.  The  general 
rule  in  charts  of  this  kind  is  that  zero  should  be 
shown  as  the  bottom  line,  or,  if  not  shown  at  the 
bottom,  that  the  omission  of  zero  should  be 
clearly  indicated.  iVs  Fig.  53  is  shown  on  a  per- 
centage basis,  the  100  per  cent  line  should  be 
clearly  indicated  by  drawing  a  broad  line  on  the 
chart  for  the  line  opposite  the  figure  100  in  the 
scale.  It  would  have  been  better,  perhaps,  to  have  plotted  the  data 
so  that  zero  would  replace  the  figure  100.  On  a  scale  so  made,  pine 
lumber  would  go  up  83  per  cent,  while  railroad  rates  would  be  shown 


American  Review  of  Revieus 

Fig.  52.  The  Increasing 
Number  of  Students  in 
the  Co-operative 
Course  of  the  En- 
gineering College  of 
the  University  of  Cin- 
cinnati 

This  illustration  was  originally 
used  as  a  companion  piece 
to  the  chart  of  Fig.  51.  For 
a  popular  exhibit  the  use  of 
vertical  bars  brings  out  in- 
formation quite  clearly. 
Though  curves  (such  as  are 
shown  in  later  chapters)  are 
superior  to  vertical  bars,  it 
is  unfortunately  true  that 
most  people  do  not  know 
how  to  read  even  the  sim- 
plest curves  correctly. 

Note  the  lettering  at  the  upper 
portion  of  the  chart.  Letter- 
ing of  this  kind  may  be  had 
by  using  separate  gummed 
letters  such  as  may  be  pur- 
chased ready  for  use 


48 


GRAPHIC    METHODS 


as  decreasing  4  per  cent.  The  scale  would  read  upward  from  the 
zero  line  for  increases,  and  downward  from  the  zero  line  for  decreases. 
By  changing  the  scale  and  using  a  broad  zero  line,  misinterpretation 
of  the  chart  would  be  entirely  prevented. 

Fig.  54  is  somewhat  similar  to  Fig.  53  in  that  intervening  years 
are  neglected,  and  that  lines  drawn  from  left  to  right  of  the  chart 
indicate  the  total  movement  rather  than  short-time  fluctuations. 
Fig.  54  w^ould  be  better  if  the  lines  around  the  outside  of  the  drawing 
had  been  omitted.  In  general,  lines  of  this  kind  around  the  outside 
of  a  chart  are  likely  to  be  confusing.  In  this  case,  the  double  lines 
at  the  bottom  of  the  chart  draw  too  much  attention  to  the  bottom 

and  may  cause  a  wrong  interpre- 
tation of  the  chart.  As  charts  of 
this  type  are  usually  made  so  as 
to  have  the  bottom  at  zero,  the 
reader  of  Fig.  54  may  get  an  en- 
tirely erroneous  idea  of  the  actual 
increase  in  the  rates  of  wages.  This 
chart  of  Fig.  54  should  have  been 
drawn  with  J/g  inch  more  room  at 
the  bottom  so  that  the  scale  would 
begin  at  zero  rather  than  at  $1.00. 
A  glance  at  the  chart  as  it  is  shown 
here  might  convey  to  any  but  a 
careful  reader  that  the  wages  of 
trackmen  had  more  than  doubled, 
within  the  period  of  ten  years 
covered  by  the  records  thus  graph- 
ically presented,  though  the  ac- 
tual wage  increase  was  only  from 
about  $1.12  to  $1.50.  Though  Fig. 
54  contains  a  good  suggestion  for 
presenting  data  in  popular  form, 
it  is  in  itself  misleading  because  it 
does  not  have  its  base  line  at  zero. 
Fig.  55  is  a  commendable  piece  of  work  for  popular  presentation, 
as  for  instance  in  a  magazine.  Note  the  use  of  dimension  marks  in 
two  independent  horizontal  rows  so  that  the  upper  row  indicates  the 
material  from  which  the  ships  are  made  while  the  lower  row  shows  the 


Reproduced  by  Permission  from  Droege's  "  Freight  Terminals  and 
Trains",  copyright,  1912,  by  the  McGraw-Hill  Book 
Companu 

Fig-  53-  Changes  after  Ten  Years  in  Costs 
of  Railroad  Materials  and  in  Freight 
Rates  for  a  Large  Railroad  System 

A  simple  chart  of  this  kind  is  often  advantageous, 
as  it  neglects  all  temporary  fluctuations  and 
shows  only  the  important  changes  over  a  period 
of  time  considered  as  a  whole.  The  line  for  100 
on  the  scale  should  have  been  made  a  broad  line 
to  indicate  the  basis  of  comparison.  A  wavy 
line  should  have  been  put  at  the  bottom  of  the 
chart  to  show  that  the  scale  does  not  begin  at  zerp 


COMPARISONS    INVOLVING    TIME 


49 


method  of  propulsion.  Dimension  lines  used  in  this  way  are  an  ex- 
tremely valuable  adjunct  to  chart  work  and  should  be  used  much  more 
commonly  than  they  are  at  present. 

Tendencies  for  the  future  are 
frequently  very  accurately  pre- 
dicted by  drawing  a  smooth  curve 
through  known  points  and  then 
continuing  this  curve  for  future 
years  in  the  manner  shown  by  the 
broad  line  in  Fig.  55.  The  trend 
of  this  curve  indicates  that  by 
1925,  we  are  likely  to  have  ships 
about  1,200  feet  long.  Though 
the  method  of  prediction  by  ex- 
tending a  curve  into  the  future  is 
very  valuable,  care  must  always  be 
used  to  apply  the  method  with 
judgment.  If  in  Fig.  55  a  curve 
had  been  drawn  from  the  data  up 
to  the  year  1860  and  extended 
from  that  point  to  show  the  prob- 
able length  of  vessels  in  succeeding 
years,  the  curve  would  have  indi- 
cated a  likelihood  of  1,200-foot 
ships  by  1870.  We  can  see  in  the 
light  of  history  that  such  a  predic- 
tion would  have  been  most  errone- 
ous. It  would  have  assumed  the 
continuance  of  side-wheel  steamers 
and  would  have  been  based  chiefly 
on  the  length  of  the  Great  East- 
ern alone.  The  Great  Eastern 
was  too  far  in  advance  of  the  age  and  was  in  reality  an  engineering 
failure.  Hence,  we  see  the  error  which  would  result  from  basing  a 
prediction  curve  on  too  limited  an  amount  of  data. 

Periodic  photographs  of  any  kind  of  construction  work  are  one 
of  the  most  striking  forms  of  graphic  presentation.  Many  large 
contractors  and  machine  manufacturers  now  make  a  practice  of 
having  photographs  taken  of  each  job  at  least  once  each  week.    The 


THE    RISING   WAGE    SCALE 

SHOWING  THAT  THE  PAY  OF  RAILROAD  EMPLOYEES 
HAS  INCREASED  FROM  30  TO  50  PER  CENT.  IN  TWELVE 
YEARS.  NOTE  THAT  THE  GENERAL  OFFICE  CLERKS 
NOW   RECEIVE   LESS  THAN   THE  TRAINMEN. 

World's  Wort 

Fig.  54.    Wage-Scale  Increase 

This  illustration  is  so  drawn  that  wages  appear  to 
have  increased  much  more  rapidly  than  is 
proved  by  the  actual  data  given  in  the  chart  it- 
self. The  chart  should  have  been  extended  to 
show  the  zero  line  of  the  vertical  scale  so  as  to 
assist  the  reader  in  getting  a  correct  interpre- 
tation 


50  GRAPHIC    METHODS 

photographs  are  carefully  dated  and  filed  for  reference  in  case  there 
should  be  any  dispute  later  regarding  the  progress  of  the  work  and 
payment  therefor.  If  a  large  card  giving  the  date  of  the  work  is  placed 
in  front  of  the  camera  so  that  the  date  is  photographed  directly  into 
the  picture,  the  date  is  somewhat  more  easily  proved  than  it  would 
be  otherwise.  Putting  the  date  card  in  front  of  the  camera  with  the 
date  upon  the  card  gives  a  chance  for  any  passer-by  to  check  the  hon- 
esty of  the  date  on  the  picture,  much  as  the  "amount  purchased" 
card  at  the  front  of  a  cash  register  checks  the  honesty  of  the  clerk. 

Progress  photographs  like  those  described  above  are  particularly 
effective  for  use  in  advertising.  A  series  of  three  or  four  pictures 
placed  one  below  another,  with  the  dates  carefully  stated  on  each, 
give  the  best  possible  demonstration  of  the  rapidity  with  which  con- 
struction work  has  been  completed  by  the  advertiser.  A  broad  use 
for  these  progress  photographs  is  found  in  the  preparation  of  reports, 
catalogues,  magazine  advertising,  etc.  Thus  a  manufacturing  plant, 
for  instance,  can  be  pictured  in  a  series  of  photographs  taken  some 
years  apart  showing  buildings  which  have  been  added  to  provide  for 
increase  in  the  business.  In  the  case  of  machinery,  a  series  of  photo- 
graphs taken  in  different  years  are  of  value  to  show  the  increase  in 
the  size  of  the  machines  built  or  the  successive  improvements  made 
in  the  design. 

Moving-picture  machines  have  opened  up  a  whole  field  of  possi- 
bilities in  the  rapid  conveying  of  accurate  information.  Many  com- 
panies are  now  using  moving-picture  films  to  show  the  technical 
operations  involved  in  making  up  their  manufactured  product,  or  to 
show  views  in  different  parts  of  a  factory.  Moving-picture  cameras 
have  been  used  also  in  a  very  striking  way  by  Mr.  Frank  B.  Gilbreth 
as  an  adjunct  to  methods  of  time  and  motion  study.  By  placing  in 
the  camera  field  with  the  worker  a  clock  with  a  large  dial  and  a  sweep- 
ing second  hand,  an  automatic  and  permanent  record  may  be  secured 
both  of  the  worker's  movements  and  the  corresponding  elapsed  time. 
The  statistics  thus  graphically  recorded  are  immeasurably  more 
accurate  and  more  conclusive  than  any  that  could  be  secured  in  any 
other  way.  Possibilities  for  the  use  of  moving-picture  machines  in 
educational  work  in  schools  are  only  beginning  to  be  grasped  by  a 
few  of  the  world  leaders  in  thought.  When  the  moving-picture  ma- 
chine becomes  a  feature  of  every  school  room  the  results  will  be  as- 
tounding. 


COMPARISONS    INVOLVING    TIME 


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Fig-  55-     The  Growth  in  the  Length  of  Ocean  Liners 

This  is  an  excellent  piece  of  presentation  for  reaching  an  average  non-technical  class  of  readers.  A  smooth 
curve  line  has  been  drawn  through  the  ends  of  the  pictured  ships  so  as  to  approximate  most  closely  the 
general  law  which  seems  to  govern  progress- in  ship  building.  The  smooth  curve  has  been  extended  into 
the  future  as  a  prediction  of  the  length  of  the  ships  which  will  probably  be  built  during  the  next  ten  years. 

Note  the  excellent  use  of  dimension-line  arrows  at  the  base  of  the  chart  showing  the  materials  used  in  ship 
building  and  the  methods  of  dri\'ing  ships  at  different  periods  in  history 

Bars  to  represent  different  intervals  of  time  as  in  Fig.  51  and 
Fig.  52  may  be  compared  to  the  progress  photographs  mentioned 
above.  Though  the  bars  and  progress  photographs  are  valuable, 
they  may  be  said  to  give  information  only  in  spots.  A  moving-picture 
machine  shows  pictures  so  rapidly  that  the  pictures  blend  into  a  con- 
tinuous narrative  in  the  eye  and  the  brain  of  the  observer.  What  the 
moving  picture  is  to  separate  progress  photographs,  the  curve  is  to 
detached  bars  representing  time.  In  just  so  much  as  the  moving 
picture  is  superior  to  separate  pictures  shown  by  lantern  slides,  in 
just  that  much  is  a  curve  superior  to  a  series  of  horizontal  or  vertical 
bars  for  the  same  data.  Unless  a  person  knows  thoroughly  how  to 
read  and  how  to  plot  curves  he  cannot  hope  to  understand  the  graphic 
presentation  of  facts.  The  use  of  curves  will  be  covered  in  later  chap- 
ters. 


52 


Chapter  IV 
TIME  CHARTS 


THE  horizontal-bar  method  used  in  Chapter  I  to  show  the  com- 
ponent parts  of  any  unit  may  be  modified  so  as  to  represent 
various   conditions   at   different   hours,   days,    and   other   sub- 
divisions of  time.     Fig.  57  ilhistrates  a  convenient  scheme  to  assist 
the  arrangement  of  vacations  for  concerns  having  many  employees,  in 
which  it  is  necessary  to  plan  the  vacations  so  that  there  shall  always 


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Fig.  57.    Chart  for  Assigning  Vacation  Periods  in  a  Large  Office 

Vacations  have  here  been  planned  so  that  not  more  than  two  men  are  away  at  any  one  time 

53 


54 


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Fig.  58.    Chart  Illustrating  Bonus  Work  in  a  Factory  where  Bonus  Work  was  Intro- 
duced Too  Rapidly  at  First 

The  curve  at  the  bottom  shows  the  total  number  of  workers  earning  a  bonus  each  day.     On  November  22 

all  the  workers  earned  a  bonus 

be  a  good  man  available  to  take  charge  of  responsible  work.  A  chart 
of  this  kind  can  be  made  quickly  if  co-ordinate  paper  is  used,  the  hori- 
zontal lines  being  drawn  in  with  lead  pencil.  Vacations  are  shifted 
around  until  an  arrangement  is  found  that  is  satisfactory  to  the  man- 
ager and  also  to  the  various  employees.  After  a  final  schedule  has 
been  decided  upon,  the  time  given  each  emploj^ee  can  be  made  sufii- 
ciently  conspicuous  by  going  over  the  lead-pencil  marks  with  crayon 
or  ink.  A  chart  of  this  nature  posted  on  the  bulletin  board  of  an 
office  would  serve  as  a  convenient  means  of  giving  information  to 
the  employees  as  to  their  respective  vacation  periods. 

Fig.  5Q  (page  52)  illustrates  a  method  regularly  used  by  Mr.  H.  L. 
Gantt  to  indicate  conditions  in  a  manufacturing  plant.  This  particular 
chart  was  drawn  to  show  progress  Aiade  in  training  the  employees 
of  a  worsted  mill  under  scientific  management.     Trained  employees 


TIME    CHARTS  55 

may  earn  a  bonus  by  completing  a  certain  quantity  of  work  each 
day.  It  will  be  seen  at  a  glance  that  the  chart  becomes  blacker  at  the 
right  hand,  thus  showing  that  two-months  training  had  greatly  in- 
creased the  output  of  the  employees.  If  a  chart  like  this  is  made 
with  different  colored  pencils,  the  facts  can  be  grasped  more  quickly 
than  when  only  one  color  is  used. 

Fig.  58,  at  the  right-hand  end,  shows  that  the  workers  were  earning 
a  bonus  practically  every  day,  and  it  also  shows  clearly  that  some- 
thing was  wrong  during  the  middle  part  of  October.  The  workers 
failed  to  earn  a  bonus  at  that  time  for  the  reason  that  the  bonus  work 
was  introduced  so  rapidly  that  they  did  not  get  adequate  instruction. 
The  manager  of  a  plant  would  realize  such  a  situation  at  once  if  he 
had  this  kind  of  a  chart  before  him. 

At  the  bottom  of  Fig.  58  a  curve  is  plotted  to  give  the  number 
of  operators  who  earned  a  bonus  every  day.  The  horizontal  scale  for 
this  curve  is  exactly  the  same  as  for  the  bar  chart  above,  except  that 
in  the  curve  a  day  is  represented  by  a  line  rather  than  by  a  space. 
In  plotting  curves,  it  is  customary  to  represent  time  by  lines  rather 
than  by  spaces,  and  this  curve  is  plotted  in  accordance  with  good 
practice.  The  scale  at  the  left-hand  edge  of  the  lower  part  of  the 
chart  represents  the  number  of  workers  who  made  the  bonus.  In 
order  to  plot  the  curve,  one  simply  counts  in  the  upper  section  of  the 
chart  the  number  of  black  blocks  which  are  filled  in  for  the  particular 
day.  Thus,  for  October  10,  we  see  that  there  are  seven  black  blocks. 
The  point  on  the  curve  is  then  placed  in  the  lower  portion  of  the  chart 
at  the  intersection  of  the  horizontal  line  representing  the  number 
of  workers  earning  a  bonus  and  of  the  vertical  line  representing  the 
day,  October  10.  The  curve  gives  a  convenient  method  of  deter- 
mining the  total  number  of  operators  who  are  earning  a  bonus.  When 
it  is  desired  to  know  only  the  number  of  employees  earning  bonus 
each  day,  the  curve  shows  the  matter  more  clearly  than  do  the  black 
blocks  in  the  upper  portion  of  the  chart.  The  horizontal  bars  give 
the  story  for  each  worker,  the  curve  gives  the  total  for  all  the  workers. 

A  chart  like  that  shown  in  Fig.  59  would  ordinarily  be  made  on 
a  long  sheet  of  co-ordinate  paper  so  that  the  co-ordinate  ruling  could 
be  used  for  the  vertical  lines,  indicating  time.  Co-ordinate  paper  in 
several  different  rulings  can  be  purchased  in  rolls  so  that  the  desired 
ruling  can  often  be  had  in  continuous  lengths.  Sometimes,  however, 
the  desired  ruling  can  be  obtained  only  in  flat  sheets  of  limited  size 


56 


GRAPHIC   METHODS 


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TIME    CHARTS  57 

and  it  is  then  necessary  to  make  a  long  sheet  by  pasting  together 
several  of  the  separate  sheets.  The  original  study  from  which  Fig.  59 
was  prepared  was  made  upon  a  built-up  sheet  seventeen  inches  wide 
and  eight  feet  long,  so  that  a  full  month  of  lighter  operation  could  be 
shown  on  the  one  chart. 

In  a  large  working  chart,  such  as  is  shown  in  Fig.  59,  very  little 
ruling  is  required  except  for  the  lines  limiting  the  width  of  the  hori- 
zontal bar  representing  each  lighter.  In  the  original  chart,  drawing 
inks  of  different  colors  were  used  to  indicate  the  four  different  condi- 
tions— working  north  and  working  south,  and  idle  north  and  idle 
south.  Black  was  used  to  indicate  towing.  Solid  red  showed  idle 
time  in  the  north,  and  a  red  made  up  of  red-ink  strokes  with  white 
spaces  showed  idle  time  in  the  south.  Thus  all  idle  time  may  be 
indicated  by  red,  the  method  of  application  determining  whether  the 
delay  is  at  the  north  or  at  the  south  end  of  the  trip.  Working  time 
may  similarly  be  indicated  by  solid  green  and  by  green  strokes  with 
white  spaces. 

It  is  desirable  in  all  chart  work  to  have  certain  conventions  by 
which  colors  would  be  understood  to  have  certain  definite  meanings. 
Thus,  following  railroad  practice,  red  could  generally  be  used  in  chart 
work  to  indicate  dangerous  or  unfavorable  conditions,  and  green  to 
indicate  commended  features  or  favorable  conditions.  Where  neither 
commendation  nor  adverse  criticism  is  intended,  colors  such  as  blue, 
yellow,  brown,  etc.,  could  be  used. 

In  Fig.  59,  an  ordinary  atomizer  filled  with  writing  ink  was  used 
to  fill  in  gray  areas  representing  night  hours.  If  a  little  care  is  used 
in  regulating  the  spray,  a  good  uniform  and  light  shade  of  gray  is 
obtained,  on  top  of  which  colored  crayons  will  show  out  clearly,  as, 
for  instance,  in  Fig.  59  where  Lighter  No.  7  is  represented  as  working 
on  the  night  of  September  23.  To  prevent  the  ink  spreading  over 
the  chart,  a  strip  of  cardboard  should  be  laid  carefully  on  each  edge 
of  the  surface  which  it  is  desired  to  ink  in  by  means  of  the  spray. 

In  making  up  charts  like  that  shown  in  Fig.  59,  the  data  are  usu- 
ally recorded  on  the  chart  day  by  day  as  reports  come  in.  This  in- 
volves a  large  amount  of  handling  of  the  chart,  and  the  chart  is  likely 
to  be  much  smeared  by  the  time  the  last  reports  are  entered.  If  col- 
ored crayons  with  the  color  embodied  in  paraffin  are  used,  very  brilliant 
colors  can  be  obtained,  yet  rubbing  with  the  hands  will  not  smear 
the  colored  areas.    Unless  a  non-smearing  crayon  is  used,  it  is  better 


58 


GRAPHIC    METHODS 


Running  LIGHT       1113 Taking  Water        g^CoAUNS 


Fig.  60.  Operations  of  Three  Tug-boats  in  New  York  for  Twenty-four  Hours.  The 
Boat  Represented  by  the  Lower  Bar  is  in  Service  for  a  Twelve-Hour  Shift  Only 

A  working  chart  of  this  kind  would  usually  be  made  on  a  long  strip  of  co-ordinate  paper.  The  illustration 
was  drawn  entirely  by  hand  to  show  the  possibilities  of  hand  cross-hatching  for  bringing  out  information 
ordinarily  showTi  in  several  colors 

to  make  up  colored  charts  by  using  different  colors  of  drawing  ink. 
The  ordinary  crayons  smear  so  badly  that  a  chart  made  with  them 
is  sometimes  unrecognizable  before  it  is  finished. 

Fig.  60  is  a  further  elaboration  of  the  method  used  in  Fig.  59. 
The  actual  chart  from  which  this  illustration  was  made  was  drawn 
on  co-ordinate  paper  ruled  in  tenths  of  an  inch.  Each  of  these  tenth- 
of-an-inch  spaces  was  made  to  represent  ten-minutes  time,  so  that  a 
much  larger  scale  was  obtained  than  in  Fig.  60.  As  the  tug-boat 
captains  regularly  kept  log-books  in  which  their  work  was  recorded 
to  a  five-minute  interval  the  chart  was  made  to  the  same  interval 
by  splitting  the  ten-minute  squares  to  represent  five-minute  intervals. 
With  a  scale  of  this  size  it  was  feasible  to  use  colored  crayons,  even 
though  some  of  the  divisions  of  time  were  very  short. 

Fig.  60  was  drawn  by  hand  and  shows  the  possibilities  in  preparing 
an  illustration  of  this  kind  when  only  one  color  of  printing  ink  is 
available. 

The  chart  from  which  Fig.  60  is  taken  was  made  to  determine  how 
much  idle  time  there  was  in  the  operation  of  three  tug-boats,  and  to 
ascertain  whether  the  boats  could  be  so  run  as  to  reduce  the  amount 
of  idle  time  and  give  better  service.  The  black  in  Fig.  60  shows  the 
idle  time  vividly.  By  looking  from  bar  to  bar,  it  is  possible  to  study 
all  the  work  of  the  three  tug-boats  and  to  determine  whether,  if  the 
work  Were  differently  assigned,  there  would  be  less  waiting  between 
jobs.  Frequently  the  tug-boats  had  to  tow  two  or  more  lighters  or 
two  or  more  car-floats,  simultaneously,  as  will  be  seen  from  the  extra 


TIME    CHARTS  59 

bars  placed  below  the  main  bar  for  each  tug.  The  number  of  lighters 
and  car-floats  towed  simultaneously  is  clearly  shown  in  the  chart,  as 
well  as  the  time  at  which  each  was  picked  up,  and  the  time  at  which 
each  was  delivered  by  the  tug.  In  the  case  of  car-floats,  a  frequent 
break  will  be  noticed  at  the  end  of  the  towing,  one-half  the  width  of 
the  horizontal  bar  being  marked  with  black.  This  convention  was 
adopted  to  show  that  the  idle  time  was  occasioned  by  the  necessity 
of  waiting  to  obtain  an  unoccupied  float  bridge  into  which  the  car- 
float  could  be  shifted.  Though  the  tug-boat  was  standing  idle  it  was 
not  feasible  for  the  dispatcher  to  take  the  tug  away  from  the  par- 
ticular car-float  to  which  it  was  attached,  for  the  tug  would  be  neces- 
sary to  place  the  car-float  in  the  float  bridge  as  soon  as  the  float  bridge 
became  free. 

Charting  of  information  frequently  brings  out  points  which  would 
be  entirely''  overlooked  if  charts  were  not  made.  The  tug-boat  chart 
from  which  Fig.  60  was  taken  at  once  calls  attention  to  the  time  re- 
quired for  the  tugs  to  obtain  water.  As  the  service  of  tugs  was  valued 
at  about  $9.00  per  hour,  the  time  spent  in  taking  water  was  a  serious 
loss.  As  soon  as  the  chart  showed  the  extent  of  this  loss,  it  was  com- 
paratively simple  to  remedy  the  situation  by  providing  different 
methods  of  getting  boiler-feed  water. 

A  time  chart  like  Fig.  60  can  often  be  used  advantageously  in 
conjunction  with  other  time  charts  covering  the  same  period  of  time. 
Thus,  in  studying  tug-boats,  the  information  on  a  chart  for  lighter 
operation  such  as  is  shown  in  Fig.  59,  and  on  charts  for  the  operation 
of  car-floats  or  of  float  bridges,  may  be  valuable.  All  the  various 
kinds  of  equipment  with  which  the  tug-boats  may  be  employed  could 
be  considered  in  the  study,  if  it  is  to  be  determined  whether  or  not 
the  most  effective  use  is  being  made  of  the  tug-boats.  If  all  the  charts 
used  in  the  study  are  drawn  to  the  same  horizontal  scale,  the  charts 
can  be  placed  immediately  above  each  other  so  that  the  operations 
of  all  related  equipment  for  every  hour  of  the  day  and  night  can  be 
instantly  seen  during  the  whole  of  a  test  period,  of,  say,  a  week  or  a 
month. 

The  charts  thus  far  considered  in  this  chapter  have  shown  time 
in  the  horizontal  direction  only.  In  Fig.  61  we  have  time  shown  by 
days  in  the  horizontal  direction  and  by  hours  in  the  vertical  direction. 
This  type  of  chart  is  extremely  valuable  in  determining  whether  or 
not   schedules   are   maintained   uniformly   over   any   period   of   time. 


60  GRAPHIC    METHODS 

By  using  different  colors  of  ink  a  chart  of  this  kind  can  be  made  so 
as  to  show  all  related  operations  without  the  drawing  becoming  too 
complex  to  read.  Fig.  61  has  purposely  been  made  simpler  than  the 
ordinary  chart  of  this  kind  to  overcome  the  handicap  of  being  limited 
to  only  one  color  of  ink  in  the  reproduction. 

Charts  in  the  form  of  Fig.  61  are  valuable  in  that  they  show  on 
one  sheet  all  the  operations  occurring  during  a  given  period  of  time — 
in  this  case,  twenty-four  hours.  Some  conditions,  such  as  the  blizzard 
of  January  7,  affect  all  the  deliveries  to  the  different  railroads.  Study 
of  the  chart  brings  out  in  contrast  conditions  which  are  beyond  the 
control  of  man  and  conditions  which  are  the  result  of  carelessness 
or  poor  management,  which  usually  crop  up  first  in  connection  with 
one  railroad,  then  in  connection  with  another,  without  being  so  gen- 
eral as  to  affect  all  of  the  curves,  as  did  the  blizzard  of  January  7. 

Fig.  62  shows  the  possibility  of  simplification  when  so  many  dif- 
ferent horizontal  curves  must  be  shown  that  easy  reading  is  impossible. 
The  simplification  is  made  in  Fig.  62  by  showing  only  one  railroad 
on  each  sheet.  All  the  figures  for  one  railroad  are  shown  in  curves, 
placed  one  above  the  other.  Ordinarily  curves  like  those  in  Fig.  62 
will  be  nearly  parallel,  for  the  time  interval  required  to  complete 
each  of  the  steps  of  work  remains  about  the  same  day  after  day.  What 
Fig.  62  brings  out  most  of  all  is  not  so  much  the  time  interval  between 
the  different  steps  as  the  information  as  to  whether  each  of  the  dif- 
ferent steps  was  started  promptly  on  schedule.  Any  one  operation 
started  late  must  delay  all  the  following  operations. 

The  paper  on  which  Fig.  62  was  drawn  is  in  itself  worthy  of  at- 
tention. This  letter-sheet  size  of  paper  was  carefully  laid  out  so  that 
a  typewriter  could  be  used  for  the  lettering  on  the  margins  of  the  four 
sides  of  the  sheet.  The  paper  was  purposely  ruled  in  squares  so  that 
any  of  the  common  divisions  of  time  might  be  shown.  The  possibilities 
in  this  direction  are: 

The  days  of  the  month  may  be  used  on  the  short  edge  of  the  paper 
as  in  Fig.  62. 

Fifty -two  weeks  for  one  year  can  be  shown  by  using  the  long  edge 
of  the  paper. 

Three  years  by  months  can  be  plotted  by  using  the  thirty-six 
squares  on  the  short  side  of  the  paper. 

One  year  by  months  can  be  shown  by  using  every  third  line  along 
the  short  edge  of  the  paper. 


TIME    CHARTS 


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Fig.  6 1 .    Operation  of  Freight  Car-Floats  at  a  Railroad  and  Steamship  Freight  Terminal 

Here  we  have  time  represented  by  days  in  the  horizontal  direction  and  by  hours  in  the  vertical  direction. 

The  object  of  the  chart  is  to  record  whether  car-floats  are  loaded  and  dispatched  at  the  same  hour  each 

day. 
Dotted  lines  show  the  time  at  which  cars  are  pushed  onto  car-floats  by  locomotives.     Solid  lines  show 

the  time  at  which  car-floats  are  towed  away  by  tug-boats.    Curves  for  any  one  car-float  destination  are 

in  pairs  bearing  the  same  letter. 
If  the  departure  schedule  is  well  maintained,  all  curve  lines  will  be  practically  horizontal.     Note  that  the 

blizzard  of  January  7  affected  the  locomotives  less  than  the  tug-boats 


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GRAPHIC    METHODS 


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Fig.  62.    Operation  of  Freight  Car-Floats  at  a  Railroad  and  Steamship  Terminal 

In  Fig.  61  several  different  railroad  connections  were  shown  on  one  large  sheet.  Here,  in  Fig.  62,  but  one 
railroad  is  represented  on  one  sheet,  with  the  idea  of  using  as  many  sheets  as  there  are  railroad  connec- 
tions. 

This  illustration  is  photographed  down  from  a  sheet  of  8^-inch  by  11-inch  co-ordinate  paper  specially 
designed  for  use  with  a  typewriter.  The  zinc  cut  for  this  illustration  was  made  directly  from  the  type- 
written original 


TIME    CHARTS  63 

Percentages  up  to  100  per  cent  can  be  indicated  by  using  fifty 
of  the  fifty-two  squares  on  the  long  dimension  of  the  paper.  This 
ruHng  gives  a  co-ordinate  paper  which  is  extremely  convenient  for 
general  work.  Other  charts  drawn  on  this  same  ruling  of  paper  may 
be  seen  in  Figs.  134,  130,  103,  156. 

Fig.  63  was  adapted  from  a  chart  shown  in  the  United  States 
Statistical  Atlas  for  the  Census  of  1900.  The  Atlas  illustration  was 
printed  in  color,  while  Fig.  63  is  in  black  ink.  The  scheme  of  this 
chart  is  one  which  could  be  used  widely,  for  it  is  an  extremely  con- 
venient method  of  showing  a  frequently  changing  rank  for  a  large 
number  of  units.  The  blocks  for  the  various  States  are  numbered 
according  to  the  rank  of  each  State  at  the  first  year  shown  at  the  left. 
The  rise  or  fall  in  rank  of  each  State  at  each  census  can  be  seen  at  once 
by  following  the  lines  joining  the  numbered  blocks.  The  actual  nu- 
merical rank  at  each  census  is  seen  by  reading  horizontally  to  the  rank 
number  at  the  right-hand  margin  or  to  the  numbers  in  the  left-hand 
column  of  blocks. 

Sales  managers  publishing  a  house  organ  may  find  the  method 
of  Fig.  63  of  great  advantage  in  showing  the  status  of  each  branch 
selling-house  or  the  rank  of  each  salesman.  If  every  member  of  the 
selling  organization  is  given  a  confidential  number,  the  rank  of  each 
can  be  shown  in  the  house  organ  sent  out  each  month.  Branch  houses 
can  be  encouraged  to  compete  with  each  other  if  their  relative  rank 
month  after  month  is  indicated  on  the  chart.  In  the  case  of  salesmen, 
if  the  numbers  are  kept  confidential  no  one  salesman  can  tell  from  the 
chart  anything  about  any  other  salesman.  He  could,  however,  see 
very  clearly  that  his  own  position  in  the  sales  force  was  getting  better 
or  worse,  according  to  whether  his  relative-rank  line  pointed  upward 
or  downward.  This  comparison  of  selling  units  on  a  rank  basis  is  in 
many  respects  fairer  than  any  curve  based  on  the  value  of  sales.  Good 
business  conditions  or  bad  business  conditions  affecting  all  alike  do 
not  show  up  in  charts  like  Fig.  63.  What  is  shown  is  the  real  progress 
or  lack  of  progress  made  by  every  man  or  branch  selling  house  as 
compared  with  all  the  others. 

Printer's  copy  for  a  chart  like  Fig.  63  can  very  easily  be  made 
up  if  printed  strips  of  the  blocks  shown  in  the  chart  are  used.  These, 
if  desired,  could  be  made  from  Fig.  63  itself.  Simply  photograph 
the  chart,  then  take  one  vertical  row  of  the  blocks,  as  for  the  year 
1900,  and  have  a  line  engraving  made  of  them,  eliminating  the  figures 


64  GRAPHIC   METHODS 

for  numbers  which  appear  in  the  middle  of  each  block.  Print  from 
the  zinc  plate  a  number  of  strips  of  blocks.  With  shears  and  a  paste- 
pot,  another  vertical  row  of  blocks  may  be  added  at  the  right-hand 
edge  of  the  chart  copy  each  month  to  provide  "copy"  for  the  plate 
to  print  the  succeeding  month's  illustration.  The  identification  could 
be  lettered  by  hand  inside  of  the  vertical  row  of  blocks  for  the  latest 
month.  It  then  takes  only  a  short  time  to  draw  lines  joining  blocks 
having  corresponding  numbers.  The  built-up  "copy"  is  then  ready 
for  the  engraver  to  make  a  zinc  plate.  Zinc  plates  cost  so  little  that 
there  is  almost  negligible  expense  required  for  the  new  line  cut  needed 
each  month. 

In  Fig.  64  the  general  scheme  of  Fig.  63  is  expanded  so  that  the 
chart  shows  not  only  the  rank,  but  also  the  comparative  size  of  the 
units  under  consideration.  This  illustration  shows  also  some  inter- 
esting combinations  of  shading  by  means  of  which  blocks  of  distinctly 
different  appearance  are  obtained.  Fig.  64  was  photographed  directly 
from  a  United  States  Government  report.  Otherwise,  the  years 
would  not  be  shown  here  reading  from  right  to  left  instead  of  from 
left  to  right.  Though  the  right-to-left  arrangement  is  unfortunate, 
the  general  scheme  of  Fig.  64  is  excellent,  as  it  gives  a  large  amount 
of  information  in  a  small  space.  The  convenience  due  to  this  method 
of  double  comparisons,  either  horizontal  or  vertical,  gives  it  a  decided 
advantage  in  clearness. 

Train  charts  like  that  shown  in  Fig.  65  are  very  commonly  used 
by  railroads,  rapid-transit  subways,  etc.  Fig.  65  would  not  look  so 
complex  if  colored  ink  were  available  to  show  in  contrast  the  express 
passenger  trains,  the  work  trains,  etc.  It  is  suggested  that  the  reader 
observe  the  key  at  the  top  of  Fig.  65  and  then  follow  a  few  of  the 
various  trains  from  one  end  of  the  line  to  the  other,  taking  into  con- 
sideration the  fact  that  this  is  a  single-track  railroad  and  that  trains 
must  pass  at  the  turnouts  which  are  available.  To  schedule  a  pas- 
senger train  such  as  that  leaving  Tyrone  at  12:25  p.  m.  is  no  simple 
proposition  on  such  a  crowded  railroad  as  this. 

In  rapid-transit  work  in  large  cities  a  time-distance  chart  in  the 
general  scheme  of  Fig.  65  is  almost  essential  if  methods  of  giving 
high-speed  service  to  the  people  are  to  be  studied.  These  time-distance 
charts  can  be  made  on  so  large  a  scale  that  two  horizontal  lines  may 
be  used  to  indicate  the  stations,  with  the  lines  spaced  a  distance  apart 
to  show  to  scale  the  actual  length  of  each  station  platform.     Time- 


TIME    CHARTS 


65 


iseo 


I870 


1880 


1890 


1900 


Rank 

'  New  York 

2  Penn. 

3  Illinois 
A  Ohio 

5  Missouri 

6  Texas 

7  Mass. 

8  Indiana 

9  Michigan 
to  Iowa 
1 1    Georgia 
iZ  Kentucky 
13  Wisconsin 
t4  Tennessee 

15  N.  Carolina 

16  New  Jersey 

17  Virginia 

18  Alabama 

19  Minnesota 

20  Mississippi 

21  California 

22  Kansas 

23  Louisiana 
248.  Carolina 

25  Arkansas 

26  Maryland 

27  Nebraska 

28  W.  Virginia 

29  Connecticut 

30  Maine 

31  Colorado 

32  Florida 

33  Washington 

34  Rhode  Isl'nd 
3B  Oregon 
seN.Hampsh'e 

37  S.  Dakota 

38  Oklahoma 

39  Indian  Ter. 

40  Vermont 

41  N.  Dakota 

42  Dist.  of  C. 

43  Utah 

44  Montana 

45  N.  Mexico 

46  Delaware 

47  Idaho 
4S  Hawaii 
49  Arizona 
BO  Wyoming 
51  Alaska 
52Nevada 

Adapted  from  the  United  States  Statistical  Atlas 

Rank  of  States  and  Territories  in  Population  at  Different  Census  Years 
from  i860  to  1900 

Each  State  is  represented  by  a  block  bearing  an  identifying  number.  The  change  in  rank  from  census  to 
census  is  indicated  by  the  connecting  lines.  Actual  rank  at  any  census  can  be  seen  by  referring  horizon- 
tally to  the  figures  at  the  right  or  to  the  figures  at  the  left. 

A  chart  of  this  kind  can  be  used  for  showing  relative  rank  of  salesmen  or  comparative  sales  of  different 
branch  sales-houses 


Fig.  63. 


66 


GRAPHIC    METHODS 


9  C"^ 


TIME    CHARTS 


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68  GRAPHIC   METHODS 

distance  curves  like  those  shown  in  Fig.  65  are  then  plotted,  one  for 
the  rear  end  and  another  for  the  front  end  of  each  train.  As  the  train 
remains  constant  in  length  throughout  one  whole  journey  it  is  obvious 
that  the  two  curve  lines  must  be  a  constant  vertical  distance  apart 
throughout  the  length  of  the  chart.  At  stations,  subway  trains  must 
stop  in  such  a  way  that  the  whole  length  of  the  train  will  be  opposite 
the  platform  so  that  passengers  may  get  in  and  out  of  every  car.  The 
trains  follow  each  other  very  rapidly,  and  it  is  essential  that  sufficient 
room  be  left  between  two  trains  for  safety.  If  two  curves  on  a  time- 
distance  chart  should  touch  each  other,  it  would  indicate  a  collision. 
The  distance  between  different  train  curves  on  a  chart  gives  informa- 
tion regarding  the  kind  of  signal  and  brake  systems  that  must  be  used 
to  give  the  desired  degree  of  safety  in  operating  the  road. 


Chapter  V 
CURVE  PLOTTING 

INFORMATION  may  be  charted  in  many  different  ways.  Under 
present  conditions,  if  six  men  were  given  a  set  of  figures  and  asked 
to  chart  these  figures,  the  six  resulting  charts  would  be  widely 
divergent  in  method.  Though  variety  in  method  of  charting  is  some- 
times desirable  in  large  reports  where  numerous  illustrations  must 
follow  each  other  closely,  or  in  wall  exhibits  where  there  must  be  a 
great  number  of  charts  in  rapid  sequence,  it  is  better  in  general  to  use 
a  variety  of  effects  simply  to  attract  attention,  and  to  present  the  data 
themselves  according  to  standard  well-known  methods. 

In  Fig.  66  the  attempt  to  give  a  spectacular  scheme  of  presentation 
seems  to  have  overshadowed  everything  else  in  the  mind  of  the  illus- 
trator. Though  a  striking  architectural  design  has  undoubtedly 
been  obtained,  the  chart  means  nothing,  for  it  is  impossible  of  inter- 
pretation. No  scale  has  been  used  in  either  the  horizontal  or  the 
vertical  direction,  as  can  be  seen  by  comparing  the  figures  on  the  block 
for  1830  with  the  figures  on  the  block  for  1840.  Even  if  some  scale 
had  been  used  in  making  up  this  chart,  the  general  scheme  is  such 
that  the  reader  would  hopelessly  flounder  in  trying  to  reach  an  accu- 
rate interpretation. 

Fig.  67  puts  the  data  given  in  Fig.  66  in  the  form  of  horizontal 
bars.  Note  that  the  values  which  the  bars  represent  are  given  inside 
of  the  bars,  for  reference  purposes.  In  order  to  make  the  shape  of 
each  bar  stand  out  distinctly,  gray  dots  were  used  which  permit  the 
figures  representing  the  values  to  be  read  through  the  shading.  This 
is  an  interesting  attempt,  but  it  is  not  satisfactory  as  a  general  scheme. 
Though  Fig.  67  gives  the  data  much  more  clearly  and  far  more  accu- 
rately than  Fig.  66,  the  method  is  not  satisfactory  because  it  is  diffi- 
cult for  the  eye  to  follow  the  ends  of  the  different  bars  in  order  to 
judge  the  increase  made  from  decade  to  decade.     The  best  method 

69 


7G 


GRAPHIC    METHODS 


134 


222 


I830 


I840 


318 


I850 


687 


I860 


829 


I870 


I504. 


seso 


164.7 


I890 


2224 


I900 


The  Philadelphia  Commercial  Museum 

Fig.  66.  Commerce  of  the  United  States  since 
1830.  The  Sum  of  Annual  Exports  and 
Imports.  Values  are  given  in  Millions  of 
Dollars 

Such  a  chart  as  this  is  worse  than  none.  There  is  no  scale 
in  either  direction.  The  block  for  1830  is  drawn  with  a 
larger  area  than  the  block  for  1840  which  represents  a 
larger  quantity.     Compare  with  Fig.  67  and  Fig.  68 


CURVE    PLOTTING 


71 


re30  Hall 


IB70  1 

S29 

1 

1880  1 

ISOd                     ■     ■  r-:^  :'i'-;:.:Ai| 

IB90  1 

I6d7                                                            ) 

of  the  three  is  followed  in  Fig.  68,  where  the  data  from  Fig.  67  are 
plotted  in  the  form  of  a  curve.  The  curve  method  brings  out  all 
the  information  in  less  space  and  in  clearer  form  than  does  the  block 

system  in  Fig.  66. 

An  understanding  of 
how  to  plot  curves  and  of 
how  to  read  them  should 
be  part  of  the  equipment  of 
every  business  man,  just 
as  it  is  of  every  engineer, 
physician,  biologist,  and 
statistician.  The  general 
scheme  of  curve  plotting 
is  so  simple  that  instruction 
in  it  should  be  given  as  part  of  the  work  in  elementary  arithmetic  in  all 
public  schools.  Children  over  ten  years  of  age  can  do  plotting  and 
can  understand  simple  curves  like  that  of  Fig.  68.  Curves  are  usually 
plotted  on  co-ordinate  paper  already  ruled  in  squares,  so  that  the  person 
doing  the  plotting  need  not  take 


Fig.  67.  Values  of  Annual  Exports  and  Imports 
of  the  United  States.  Figures  are  Given 
in  Millions  of  Dollars 

This  chart  is  drawn  to  scale  from  the  data  given  in  Fig.  66, 
to  show  the  use  of  horizontal  bars  for  work  of  this  nature 


MiLUONS  n 
OK       -^ 
Dollars 


o        -^ 

I/)  CO 


/ 

/ 

/ 

J 

■^ 

/ 

/ 

/ 

> 

^ 

y 

■ 

/ 

^ 

the  time  necessary  to  rule  the 
paper.  For  reports,  for  illustra- 
tions of  magazine  articles,  or  for 
advertising,  it  is  ordinarily  better 
to  rule  by  hand  a  small  area  such 
as  is  shown  in  Fig.  68  so  that  the 
spacing  of  the  ruling  may  suit  ex- 
actly the  data  which  it  is  desired 
to  plot. 

In  Fig.  68  we  have  data  avail- 
able only  by  decades,  from  1830  to 
1900  inclusive.  Lines  are  drawn 
vertically  for  each  decade.  The 
scale  need  not  run  above  2,300,  for 
the  largest  figure  to  plot  is  2,244 
millions.  A  suitable  scale  is  secured 
by  using  one  line  for  each  200  millions.  After  the  background  ruling 
has  been  drawn,  the  figures  at  each  census  are  laid  off  to  scale,  on 
the  proper  vertical  lines  to  represent  census  years,  and  a  dot  is 
placed  on  each  vertical  line  at  that  vertical  distance  which  represents 


2200 
2000 
1800 

ieoo 

1400 
1200 
lOOO 
800 
600 
400 
200 


1630     40        50       '60      "70       "SO      '90     130O 

Fig.  68.  Value  of  Annual  Exports  and 
Imports  of  the  United  States.  Fig- 
ures are  Given  in  Millions  of  Dollars 

This  curve  is  drawn  from  the  same  data  as  Figures 
66  and  67.  The  curve  shows  the  changes 
from  decade  to  decade  more  vividly  than  do 
the  horizontal  bars  of  Fig.  67 


72  GRAPHIC    METHODS 

the  data  according  to  the  scale  chosen.  Thus  the  figure  222  for  the 
year  1840  would  be  indicated  as  a  dot  on  the  vertical  line  for  1840 
slightly  above  the  place  where  the  horizontal  scale  line  for  200  crosses 
the  chart.  After  the  dots  for  decade  years  have  been  placed  on  the 
vertical  lines,  the  dots  are  joined  with  a  heavy  line  and  a  curve 
appears. 

The  curve  of  Fig.  68  shows  the  changes  from  decade  to  decade 
much  better  than  the  bars  of  Fig.  67.  It  can  be  seen  at  once  from 
the  curve  that  the  greatest  gain  in  any  decade  was  between  1870 
and  1880  when  the  increase  was  three  and  a  half  divisions  on  the  ver- 
tical scale.  The  bars  in  Fig.  67  have  no  horizontal  scale  to  measure  by 
and  the  comparison  between  census  years  is  accordingly  more  difficult. 

When  plotting  any  curve  the  vertical  scale  should,  if  possible,  be 
chosen  so  that  the  zero  of  the  scale  will  appear  on  the  chart.  Other- 
wise, the  reader  may  assume  the  bottom  of  the  chart  to  be  zero  and 
so  be  grossly  misled.  Zero  should  always  be  indicated  by  a  broad 
line  much  wider  than  the  ordinary  co-ordinate  lines  used  for  the 
background  of  the  chart. 

In  Fig.  68,  it  will  be  noticed  that  figures  are  given  at  the  top  of 
the  chart  to  represent  the  value  for  each  point  plotted  on  the  curve. 
The  use  of  figures  at  the  top  of  the  chart  in  this  manner  is  very  de- 
sirable. The  figures  are  in  plain  sight,  so  that  anyone  desiring  to 
know  the  value  of  any  point  on  the  curve  can  look  above  the  point 
to  get  the  actual  figure  wanted,  without  having  to  read  from  the  scale 
at  the  left-hand  edge  and  then  estimate  roughly  the  value  for  any 
point  which  happens  to  fall  in  a  space  between  two  horizontal  lines 
of  the  scale.  Reading  from  the  figures  at  the  top  of  the  chart  permits 
any  desired  figure  to  be  obtained  more  rapidly  and  much  more  accu- 
rately. In  addition  to  this,  the  figures  are  recorded  in  such  manner 
that  they  may  be  quoted  for  use  elsewhere  by  anyone  who  may  wish 
to  make  use  of  the  data  in  a  speech  or  in  a  written  article  in  which 
the  chart  itself  cannot  be  used. 

It  would  be  a  desirable  thing  if  in  all  curve  charts  the  figures  for 
the  horizontal  scale  were  placed  at  the  bottom  of  the  chart  rather  than 
at  the  top.  Many  illustrations  in  this  book,  taken  from  publications 
of  excellent  standing,  show  dates  (such  as  years,  months,  etc.)  at  the 
top  of  the  chart.  If  the  horizontal  scale  were  always  placed  at  the 
bottom,  the  standard  arrangement  would  be  a  convenience  to  the 
reader  and  would  give  the  additional  advantage  that  the  top  of  the 


CURVE    PLOTTING 


73 


chart  would  be  free  for  a  numerical  statement  such  as  is  found  at  the 
top  of  Fig.  68. 

The  scales  of  any  curve  chart  should  be  so  selected  that  the  chart 
will  not  be  exaggerated  in  either  the  horizontal  or  the  vertical  direc- 
tion. It  is  possible  to  cause  a  visual  exaggeration  of  data  by  care- 
lessly or  intentionally  selecting  a  scale  which  unduly  stretches  the 
chart  in  either  the  horizontal  or  the  vertical  direction.  Just  as  the 
English  language  can  be  used  to  exaggerate  to  the  ear,  so  charts  can 
exaggerate  to  the  eye. 

A  curve  permits  of  finer 
interpretation  than  any 
other  known  method  of 
presenting  figures  for  anal- 
ysis. Fig.  69  gives  some 
information  which  many 
persons  might  not  fully 
grasp  if  only  a  column  of 
figures  were  used  to  indicate 
the  average  yearly  earnings 
of  Princeton  graduates.  The 
fairly  uniform  slope  of  the 
curve  for  the  first  six  years 
after  graduation  indicates 
that  the  men  were  receiving 
almost  uniform  raises  in  pay  each  year.  It  must  be  remembered  that  a 
straight-line  curve  simply  indicates  that  the  amounts  of  the  increases 
year  by  year  are  uniform  in  numerical  value.  If  a  curve  were  started  at 
the  lower  left-hand  corner  of  the  chart  and  drawn  diagonally  across  each 
of  the  rectangles  of  the  chart,  it  would  be  seen  at  once  that  there 
would  be  a  straight  line  indicating  an  increase  in  salary  of  $500  per 
year.  With  such  a  straight  line  across  the  chart,  the  increase  in  salary 
for  the  first  year  would  be  $500.  As  compared  with  a  zero  beginning- 
wage  there  would  be  an  increase  of  an  infinite  percentage  at  the  end 
of  the  first  year.  The  next  year  the  increase  would  again  be  $500. 
Compared  to  the  $500  salary,  the  increase  w^ould  be  100  per  cent. 
The  third  year  the  increase  would  be  $500,  and  compared  to  a  $1,000 
salary  the  increase  would  be  only  50  per  cent.  A  curve  of  uniform 
slope  on  any  chart  of  rectangular  co-ordinate  lines  indicates  only  that 
there  has  been  a  uniform  increase  or  decrease  in  actual  numbers,  not 


Fig.  69.  Average  Income  of  155  Princeton  Grad- 
uates of  the  Class  of  1901  for  Ten  Years  After 
Graduation 

Note  the  effect  of  the  1907  panic  on  incomes  in  1908 


74 


GRAPHIC    METHODS 


values  given  in  Millions  of  Uolldlj 


■PRODUCTION 


a  uniform  rate  of  change  on  a  percentage  basis.  A  plotted  line  repre- 
senting a  uniform  rate  of  increase  from  year  to  year  on  a  percentage 
basis  may  be  seen  in  the  curve  given  in  Fig.  121. 

The  untrained  reader  of 
curves  will  probably  not  be 
able  to  tell  instantly  what 
made  the  flat  portion  of  the 
curve  in  Fig.  69  during  the 
year  1907  to  1908.  One  of 
the  chief  advantages  of  the 
curve  method  of  presenting 
information  is  that  a  curve 
forces  one  to  think.  A 
little  thought  here  will  at 
once  bring  out  the  fact  that 
the  flattening  of  the  curve 
was  caused  by  the  1907 
panic.  Though  the  panic 
started  in  October  of  the 
year  1907,  the  year  1907 
was  really  one  of  the  most 
prosperous  years  the  coun- 
try has  ever  known.  It 
IMPORTS  2  w^ould  be  more  fitting  if  the 

panic  were  called  the  1908 
panic,  since  the  main  effect 
of  the  panic  came  in  1908 
rather  than  in  the  year 
1907.  It  can  be  seen  that 
the    Princeton     men     had 

Fig.  70.  Cotton  Goods  Production,  Import  and  their  incomes  reduced  dur- 
Export  for  the  United  States.  Values  are  ing  the  year  1908  so  that 
Given  in  Millions  of  Dollars  ^j^^  average  fell  below  that 

The  order  of  years  here  reading  from  right  to  left  gives  the         j?   -,  ^^ry         "D       1       ^  '  1 

first  impression  that  production  is  decreasing.     Compare      OI    1907.       xJy  lOOKlUg  alOUg 
this  illustration  with  Fig.  71  ^j^^  ^^^^^  .^  ^^.jj  ^^  noticcd 

that  though  there  was  a  larger  yearly  increase  in  salary  after  1909, 
salaries  at  the  end  of  1911  had  not  attained  the  point  which  it 
would  seem  they  would  naturally  have  reached  if  no  panic  had 
occurred  at  a  time  so  shortly  preceding  this  date. 


[L 


EXPORTS 


rmTi 


Cotton  Goods 

The  Philadelphia  Commercial  Museum 


CURVE    PLOTTING 


75 


Millions 

Dollars 

360 


In  Fig.  70  vertical  bars  have  been  placed  touching  each  other, 
with  the  earlier  years  at  the  right.  The  whole  arrangement  of  the  chart 
is  extremely  poor  and  also  misleading.  In  Fig.  71  the  data  of  Fig. 
70  have  been  replotted.  The  most  striking  thing  about  Fig.  71  is 
the  falling  off  in  the  rate  of  increase  of  production  in  the  decade 
between  1870  and  1880.  The  shape  of  the  curve  at  once  starts  a  train 
of  thought  in  regard  to  tariff  legislation  and  other  conditions  which 
may  affect  the  manufacture  of  cotton  goods. 

It  will  be  noticed  in  Fig.  71  that  we  have  four  curves,  while  only 
three  sets  of  bars  were  given  in  Fig.  70.  It  is  evident  that  if  we  add 
production  and  imports  and  then  deduct  exports,  we  will  have  a  fair 
indication  of  consumption  if  the  amounts  remaining  in  warehouses, 
etc.  (which  are  probably  a  negligible  percentage  of  the  whole  con- 
sumption) are  excepted.  Note  that. the  import  and  export  curves  follow 
each  other  in  general  form, 
though  the  export  curve 
fluctuates  on  a  percentage 
basis  much  more  rapidly 
than  does  the  import  curve. 
Remember  that  in  the  fluct- 
uations of  two  curves  like 
these,  the  change  from  year 
to  year  must  be  judged 
from  the  zero  base  line 
rather  than  from  the  slope 
of  the  curves  themselves. 
The  drop  in  the  export 
line  from  1860  to  1870  was 
almost  one-half,  while  the 
drop  in  the  import  line  for 
the  same  period  was  much 
less  than  one-half,  even 
though  the  import  line 
does  show  the  greater  slope 
downward. 

In  Fig.  72  we  have  an  example  of  what  not  to  do  in  charting. 
The  main  effect  of  the  circles  is  to  give  one  a  headache  without  per- 
mitting any  accurate  comparison  between  the  years.  The  eye  does  not 
easily  see  each  circle  as  an  area.     The  tendency  is  to  see  only  rings 


/ 

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exports,. 

SB 

Fig.  71. 


Cotton  Goods  Production,  Import  and 
Export  for  the  United  States 

These  curves  are  plotted  from  the  data  of  Fig.  70,  and  show 
the  information  in  much  clearer  form 


76 


GRAPHIC    METHODS 


between  the  lines  of  the  circles, 
rather  than  the  whole  area  in- 
cluded inside  of  each  circle  line. 

Fig.  73  gives  the  data  of  Fig. 
72  in  curve  form.  The  heavy  solid 
line  curve  shows  the  changes  from 
decade  to  decade  as  they  could 
never  be  interpreted  from  either 
the  actual  figures  or  the  circles  of 
Fig.  72.  The  tremendous  increase 
in  the  world's  commerce  between 
1900  and  1910  is  of  very  great 
interest,  showing  the  effect  which 
better  means  of  communication 
have  brought  about  as  a  result  of 
the  splendid  increase  in  scientific 
and  engineering  knowledge. 

If  one  makes  comparisons  be- 
tween the  circles  of  Fig.  72  on  a 


Biiiionb  ot 
Dolloro 


The  Philadelphia  CommeTCial  Mtisevm 

Fig.  72.  Annual  Commerce  of  the  World, 
Imports  and  Exports  Combined. 
Shown  at  Ten-year  Periods,  1850- 
1910 

These  circles,  drawn  on  an  area  basis,  are  even  more 
difBcult  to  interpret  than  the  circles  of  Fig.  38. 
The  eye  is  likely  to  see  the  rings  rather  than  the 
whole  areas  of  the  circles.     Compare  Fig.  73 


/ 

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.-- 

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SB 

1870         1880         I09O         I900 


1910 


The  Philadelphia  Commercial  Museum 

Fig.  73.  Annual  Commerce  of  the  World, 
Imports  and  Exports  Combined. 
Shown  at  Ten-year  Periods,  1850- 
1910 

The  solid  line  is  plotted  according  to  the  figures 
given  in  Fig.  7i.  The  dotted  line  shows  the 
erroneous  impression  which  would  be  obtained 
by  the  reader  if  he  should  interpret  Fig.  72  by 
the  diameters  instead  of  by  the  areas  of  the 
circles 

diameter  basis  rather  than  on  the 
area  basis  to  which  the  circles  were 
drawn,  one  gets  an  interpretation 
like  that  indicated  by  the  dotted 
line  in  Fig.  73.  By  comparing  the 
dotted  line  with  the  solid  curve 
the  reader  may  see  the  extent  of 
the  error  which  arises  if  circles  are 
compared  on  a  diameter  basis  after 
being  drawn  on  an  area  basis. 

Fig.  74  gives  a  good  idea  of  the 
utility  of  the  curve  method  for 
showing  concisely  a  large  quantity 
of  data.  If  the  figures  for  the  price 
of  cement  had  been  expressed  in 
dollars  and  shown  in  a  long  numer- 
ical column,  there  would  be  very 
few  readers  who  would   take  the 


CURVE    PLOTTING 


77 


trouble  to  follow  the  table  of  figures  and  notice  the  fluctuations  from 
year  to  year.  The  curve,  however,  gives  all  the  variations  in  price 
at  a  glance  and  shows  in  most  striking  manner  the  great  reduction 
which  occurred  in  the  price  of  cement  as  manufacturing  facilities  im- 
proved and  increased.  A  curve  of  this  kind  greatly  stimulates  thought, 
for  one  immediately  wishes  to  know  the  cause  of  each  of  the  peaks 
and  of  each  of  the  valleys  in  the  curve.  One  gets  a  vista  of  recurring 
periods  of  financial  boom  and  of  financial  depression,  and  a  glimpse 
of  such  factors  as  new  developments  in  methods  of  manufacturing 
cement  and  the  constantly  increasing  demand  for  the  product. 

If  the  reading  of  curves  were  understood  by  the  average  educated 
person,  it  would  be  possible  to  use,  in  almost  any  kind  of  magazine, 
advertising  illustrations  on  the  order  of  that  shown  in  Fig.  75.  Since, 
however,  curves  are  not 
widely  understood  at 
present,  this  type  of 
advertising  must  now 
be  limited  chiefly  to 
the  technical  journals 
read  by  engineers  and 
others  who  understand 
curve  interpretation. 
It  is  really  a  calamity 
that  curves  are  not 
more  widely  under- 
stood. Advertising  men 
are  now  frequently  un- 
able to  convince  people  of  their  argument  simply  because  they  have 
no  language  by  means  of  which  figures  can  be  made  interesting  or 
even  intelligible  when  expressed  in  an  advertisement  of  limited  size. 
The  author  ventures  to  predict  that  it  will  be  only  a  very  few  years 
until  curves  are  so  widely  understood  and  used  that  they  may  be 
presented  advantageously  in  any  high-grade  advertising  pages. 

It  would  be  almost  impossible  to  give  a  clear  idea  of  the  flood 
indicated  in  Fig.  76  if  only  columns  of  figures  were  used.  With  the 
curve  it  can  be  seen  clearly  that  the  stream  rose  very  rapidly  and 
subsided  rapidly,  so  that  the  stream  was  down  almost  to  normal 
level  within  forty -eight  hours  after  the  beginning  of  the  flood.  This 
curve  was  probably  plotted  from  flood-gauge  readings  taken  once  an 


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Fig.  74.    Prices  of  Cement,  per  Barrel,  in  Bulk,  at  the 
Mill,  from  1880  to  19 10 

Columns  of  printed  figures  or  a  series  of  vertical  bars  could  not  por- 
tray this  information  as  vividly  as  it  is  brought  out  by  the  curve 
shown  above 


78 


GRAPHIC    METHODS 


hour,  or  even  more  frequently.  The  curve,  therefore,  was  plotted 
on  much  more  numerous  points  than  are  indicated  by  the  vertical 
lines  of  the  horizontal  scale.  Frequent  observations  of  the  gauge 
height  and  the  numerous  points  plotted  on  the  curve  in  Fig.  76  ex- 
plain those  fluctuations  in  the  line  of  the  curve  which  occur  in  the 
spaces  between  the  vertical  lines.  Ordinarily  a  chart  is  sufficiently 
accurate  if  straight  lines  are  drawn  from  point  to  point  of  the  plotted 
data  for  a  curve,  without  attempting  to  make  a  smooth,  flowing  line. 


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Fig.  75.  Advertising  Illustration  used  in  a  Technical  Magazine,  »with  a  Heavy-type 
Statement  Proclaiming  that  "3000  Central  Stations  in  the  United  States  need  a 
High  Grade  Gasoline-Electric  Generating  Set" 

The  black  areas  indicate  the  portion  of  the  24-hour  power-house  load  for  which  the  gasoline  engine  would 
be  used 

The  curve  looks  smooth  in  this  illustration  simply  because  the  gauge 
readings  were  taken  so  frequently  that  the  nearness  of  the  many 
points  made  the  lines  joining  them  appear  curvilinear  rather  than 
angular.  Such  a  smooth  curve  would  not  have  resulted  if  gauge  read- 
ings had  been  taken  only  every  six  hours  and  the  chart  made  by  con- 
necting with  straight  lines  the  points  plotted  for  the  data  obtained  at 
these  longer  intervals. 

Another  flood  curve  is  shown  in  Fig.  77.  The  speed  wuth  which 
the  water  ran  off  the  territory  drained  can  be  judged  by  the  shape 
of  the 'curve.  It  is  not,  however,  safe  to  compare  the  shapes  of  the 
curves  in  Fig.  76  and  Fig,  77  without  noticing  that  in  Fig.  77  we  have 
one  day  represented  by  a  space  approximately  the  same  as  the  space 
used  in  Fig.  76  for  only  six  hours.  If  the  curve  of  Fig.  76  were  plotted 
on  the  same  horizontal  scale  as  the  curve  of  Fig.  77,  the  flood  would 
appear  to  be  much  more  severe  and  rapid  than  it  appears  from  Fig.  76. 


CURVE    PLOTTING 


79 


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Sepf.6fh  Sept.  7th.  Septdfh 

Time  in  Hours 

Engineering  Record 

Fig.  76.    Curve  Showing  Duration  of  a  Flood,  September  16,  1909, 
in  the  Canadian  River,  New  Mexico 

This  curve  was  first  plotted  on  a  paper  having  co-ordinate  lines  close  together.     For 
ease  of  reading,  the  intermediate  lines  were  omitted  from  the  magazine  illustration 

In  general,  it  is  unwise  to  compare  the  shapes  of  two  curves  unless 
they  are  plotted  to  the  same  scales,  both  horizontal  and  vertical. 

The  curve  of  Fig.  77  is  misleading  because  the  scale  does  not  begin 
at  zero.     Only  the  peak  of  the  flood  is  shown,  with  no  zero  line  from 

which  to  judge  the 
extent  by  which  the 
flood  exceeded  the 
normal  flow  of  the 
river.  If  the  co-ordi- 
nate lines  were  drawn 
so  as  to  show  the  zero 
hne,  the  base  of  the 
chart  would  be  about 
5^  inch  lower  than  it 
appears  in  Fig.  77,  and 
the  whole  curve  would 
make  a  different  im- 
pression. The  omission 
of  the  zero  line  in  charts 
of  this  kind  is  partic- 
error  made   by  persons 


iOOOO   24       25      26      27      28      29      JO      31         I        2 

April 

Enginetring  Record 

Fig.  77.    Flood  in  the  Hudson  River  at  Mechanics- 
ville,  N.  Y.,  March,  1913 

Note  the  different  scales  at  the  right  and  the  left  by  which  the 
curve  may  be  interpreted.  This  chart  is  misleading  because  the 
scales  do  not  begin  at  zero 


IS   a   very  common 


ularly  irritating,  yet  it 
drawing  charts. 

Note  that  in  Fig.  77  the  curve  can  be  read  from  two  distinct  scales, 
one  scale  on  the  left  side  of  the  chart,  and  a  different  scale  on  the 


80 


GRAPHIC    METHODS 


right  side  of  the  chart.  If  only  one  scale  is  used,  it  should  be  placed 
at  the  left-hand  side  of  the  chart.  In  very  large  charts  it  is  some- 
times desirable  to  repeat  the  scale  at  the  right-hand  side  as  well. 
Where  two  different  units  of  measurement  are  used  in  the  scales, 
the  units  should  be  carefully  named  so  that  there  will  be  no  danger 
of  the  reader's  using  the  right-hand  and  the  left-hand  scales  inter- 
changeably as  though  they  represented  the  same  unit. 

Charts  like  that  shown  in 
Fig.  78  are  quite  frequently 
used  in  public  health  reports. 
It  is  difficult  to  see  how  such 
an  unsatisfactory  type  of 
chart  ever  came  into  general 
use,  unless  it  was  because 
there  are  twelve  months  in  a 
year  and  twelve  hours  on  the 
face  of  a  clock.  If  the  death 
rates  for  the  different  months 
of  the  year  were  plotted  in  a 
curve,  using  rectangular  co- 
ordinates, the  data  would  be 
just  as  easy  to  read  and  to 
understand  as  when  shown  by 
the  radial  scheme  (polar  co- 
ordinates) of  Fig.  78.  There 
would  be  the  additional  ad- 
vantage that  the  rectangular 
method  would  be  more  widely  understood  than  the  circular  method 
of  Fig.  78. 

Though  a  chart  in  the  form  of  Fig.  79  might  be  justified  in  the 
Sunday  supplement  of  a  newspaper  where  an  untrained  audience  must 
be  reached,  it  is  much  better  to  use  a  curve  in  the  form  of  Fig.  80 
whenever  a  trained  audience  is  assured.  The  most  interesting  thing 
about  Fig.  79  is  the  slanting  line  which  gives  an  unusual  optical  illusion 
if  observed  under  artificial  light,  especially  with  a  bare  gas  flame. 
The  slanting  line  then  appears  blue,  although  it  is  printed  black  like 
the  horizontal  bars  of  the  chart. 

The  dotted  line  in  Fig.  80  corresponds  to  the  slanting  line  of  Fig. 
79,  and  represents  a  progressive  average  of  all  the  points  on  the  curve 


United  States  Statistical  Atlas  of  the  1900  Census 

Fig.  78.  Death  Rate  from  Consumption  per 
1000  Inhabitants  for  Each  Month  of  the 
Year  in  Cities  of  the  United  States 

This  type  of  chart  should  be  banished  to  the  scrap  heap. 
Charts  on  rectangular  ruling  are  easier  to  draw  and 
easier  to  understand 


CURVE    PLOTTING 


81 


above.  The  dotted  line,  of  course,  coincides  with  the  solid  line  at  the 
first  point  Avhere  there  is  only  one  point  to  consider  in  the  average. 
Figures  for  the  dotted  line  are  obtained  by  averaging  the  figures  for 
the  first  two  years,  then  the  first  three  years,  then  the  first  four  years, 
etc.,  until  the  last  point  on  the  dotted  line  represents  an  average  for 
all  the  points  on  the  solid  line. 

Fig.  80  is  worthy  of  attention  as  a  model  of  good  practice  which 
may  be  studied   carefully  by  anyone   just  beginning   to   plot  curves. 


Pittsburgh  and  Lake  Erie  Railroad 

Fig.  79.    Yearly  Average  of  Revenue  Tons  per  Train  Mile  on  the  Pittsburgh  and  Lake 
Erie  Railroad.    The  Slanting  Line  Shows  a  Progressive  Average 

If  this  illustration  is  observed  with  artificial  light,  an  interesting  optical  illusion  may  be  noticed  in  that  the 

slanting  line  appears  blue  in  color 
The  use  of  horizontal  bars  here  gives  a  chart  less  easy  to  interpret  than  the  curve  shown  in  Fig.  80  for  these 

same  data 


82 


GRAPHIC    METHODS 


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Fig.  8o.    Yearly  Average  of  Revenue  Tons  per  Train  Mile  on  the  Pittsburgh  and  Lake 
Erie  Railroad.    The  Slanting  Line  Shows  a  Progressive  Average 

Here  we  have  the  data  of  Fig.  79  plotted  in  a  curve  which  can  be  interpreted  easily  and  accurately 
This  chart  may  be  considered  a  model  of  good  practice  in  curve  plotting.     All  of  the  work,  including  the 
lettering,  has  been  done  by  hand,  thus  insuring  belter  results  than  can  usually  be  obtained  from  printing 

The  following  features  of  Fig.  80  are  pointed  out  for  the  benefit  of 
anyone  who  may  have  curves  to  plot: 

1.  The  zero  line  is  a  much  broader  line  than  the  co-ordinate 
lines.   . 

2.  Heavy  lines  are  not  used  at  the  right-  and  left-hand  edges, 
since  the  chart  does  not  start  or  end  at  the  beginning  or  end  of 
time. 

3.  All  lettering  is  so  made  that  it  can  be  read  horizontally  or 
from  the  right-hand  edge  of  the  sheet. 

4.  Years  are  given  with  four  figures  for  every  tenth  year 
ending  in  zero.  Other  years  are  indicated  with  two  figures  so  that 
they  may  be  more  quickly  read. 


CURVE    PLOTTING  83 

5.  All  letters  and  figures  on  this  chart  were  made  by  hand, 
showing  the  perfection  which  may  be  attained  by  practice  in 
lettering. 

6.  The  curve  itself  stands  out  clearly  from  the  co-ordinate  lines. 

7.  Figures  at  various  points  along  the  curve  indicate  matters, 
which  are  worthy  of  special  notice.  Foot  notes  are  not  given 
here,  however,  as  they  are  only  of  highly  technical  interest. 

8.  Figures  for  the  values  of  points  on  the  main  curve  are  given 
at  the  top  of  the  chart  immediately  above  each  corresponding 
point  on  the  curve.  Values  may  be  read  correctly  from  the  upper 
figures  rather  than  guessed  at  by  estimating  them  roughly  on  the 
left-hand  scale. 

9.  The  statement  "Revenue  Tons  per  Train  Mile"  at  the  upper 
left-hand  corner  is  purposely  printed  diagonally  so  that  it  may 
serve  as  a  heading  for  each  of  the  two  columns  of  figures,  one  at 
the  left  and  the  other  at  the  top  of  the  chart.  The  diagonal  ar- 
rangement gives  a  neater  effect  than  can  be  obtained  otherwise. 

10.  Though  figures  for  the  dotted  curve  could  be  shown  at 
the  top  of  the  chart  the  dotted  line  is  of  only  minor  interest  here. 
It  is  accordingly  best  to  avoid  the  two  columns  of  figures  at  the 
top  in  order  that  the  figures  for  the  main  curve  may  stand  out 
more  prominently. 


Chapter  VI 
CURVE  PLOTTING  CONTINUED 

THERE    are  so  many  different  applications  of  curves  and  such 
varied  yet  convenient  methods  of  plotting  curves,  that  it  seems 
worth  while  to  take  up  some  of  these  in  detail,  and  point  out 
certain    advantages    and    disadvantages    of    different    curve-plotting 
schemes. 

Practically  all  curves  display  relations  existing  between  different 
sets  of  data  which  we  may  call  "  variables".  One  of  the  variables 
is  used  as  a  standard  or  measure  by  which  to  interpret  the  facts  under 
consideration,  and  it  may  be  called  the  "independent  variable".  The 
other  variable,  which  is  interpreted  from  the  independent  variable,  is 
called  the  "dependent  variable".  For  example,  in  a  bacteriological 
examination  of  a  pond  at  varying  depths,  distance  below  the  surface 
would  be  the  independent,  and  number  of  bacteria  per  cubic  centimeter 
the  dependent  variable.  In  a  seasonal  gauging  of  a  stream  the  dates  of 
observation  would  be  the  independent  and  cubic  feet  per  second  of 
flow  the  dependent  variable.  Sometimes  we  consider  more  than  two 
variables  simultaneously,  and  we  then  have  two  or  more  independent 
variables  from  which  to  consider  a  dependent  variable. 

It  is  difficult  to  make  a  general  rule  for  determining  in  any  case 
which  is  the  independent  variable  and  which  is  the  dependent  variable. 
The  decision  depends  entirely  on  how  any  set  of  data  is  approached 
and  on  the  habits  of  mind  of  the  investigator.  When  time  is  one  of 
the  variables  it  is  usually,  but  not  always,  the  independent  variable. 
If  we  consider  values  or  quantities  at  different  dates,  as  in  Fig.  80, 
time  is  very  obviously  the  independent  variable.  If,  however,  we  are 
interested  in  the  length  of  time  required  to  do  different  operations,  as 
in  Fig.  85,  Fig.  86,  and  Fig.  87,  our  data  are  expressed  in  length  of 
time  and  time  is  the  dependent  variable.  This  example  is  an  excep- 
tional case  and  it  is  named  here  only  to  show  that,  although  time  is 

84 


CURVE    PLOTTING  85 

ordinarily  the  independent  variable  when  it  enters  into  curve  plotting, 
nevertheless  there  may  be  occasions  when  time  is  the  dependent 
variable,  and  charts  should  be  plotted  accordingly.  It  is  important 
that  the  person  drawing  a  chart  should  in  each  case  distinguish  be- 
tween the  independent  variable  and  the  dependent  variable,  for  this 
distinction  affects  the  whole  arrangement  of  the  chart. 

It  should  be  a  strict  rule  for  all  kinds  of  curve  plotting  that  the 
horizontal  scale  must  be  used  for  the  independent  variable  and  the 
vertical  scale  for  the  dependent  variable.  When  the  curves  are  plotted 
by  this  rule  the  reader  can  instantly  select  a  set  of  conditions  from 
the  horizontal  scale  and  read  the  information  from  the  vertical  scale. 
If  there  were  no  rule  relating  to  the  arrangement  of  scales  for  the 
independent  and  dependent  variables,  the  reader  would  never  be 
able  to  tell  whether  he  should  approach  a  chart  from  the  vertical 

scale  and  read  the  information  from  the  hori- 
zontal scale,  or  the    reverse.      If  charts  are 
I  '"'{  /izsoo  always  plotted  with  the   independent  varia- 

ble as  the  horizontal  scale,  there  need  be  no 
question  in  the  reader's  mind  as  to  how  he 
should  interpret  the  chart.  The  rule  for  scale 
arrangement  is  not  always  followed,  and  a 
so- OFF  PIER -A-  few  examples  are  shown  here  to  indicate  the 

HUDSON  RIVER  Trr»  1  P       •  •  I'll 

{SAMPLES  J50  TO  35s)  Qitticulty  ot  mtcrprctatiou  which  the  reader 

Meno,oiuanse.a^eco^rn^u.ion       ^^^y  havc  just  bccausc  a  rathcr  simple  prin- 
os New  York,  1912       c^pJe  of  curvc  plotting  has  been  neglected. 

^ieria-  pfr'Tubic"cf:«:  I"  ^ig.  81   the  depth   of   the   water  has 

meter  of  Hudson  River     been  plotted  downward   from  the  top  of  the 

Water  at  New  York  at     chart  so  that  the  reader  may  get  the  impres- 
Different  Depths    below       .  „  i  i.«.  i. 

the  Surface  ^i^^   ^^  measurements  taken  at  difterent  dis- 

tances below  the  surface  of  the  water.  In 
making  the  tests  which  are  represented  in  Fig.  81,  different  depths 
below  the  surfaces  were  selected  and  the  bacteria  determined  from 
the  water  samples  taken  at  these  depths.  The  depth  is  here  the  in- 
dependent variable,  and  bacteria  per  cubic  centimeter  the  dependent 
variable.  The  decision  as  to  which  is  the  independent  variable  and 
which  is  the  dependent  variable  rests  entirely  on  how  the  problem  is 
approached.  Numerous  samples  could  have  been  taken  at  different 
depths,  and  then  a  curve  plotted  to  determine  the  depth  at  which 
certain  numbers  of  bacteria  per  cubic  centimeter  were  found.     In 


7.SOO 


86  GRAPHIC    METHODS 

such  a  case,  bacteria  per  cubic  centimeter  would  be  the  independent 
variable  and  depth  would  be  the  dependent  variable.  This  sort  of 
problem  may  be  attacked  from  either  one  standpoint  or  the  other, 
and  it  is  just  a  question  of  convenience  as  to  which  method  is  used 
and  which  variable  is  made  the  independent  variable.  Though  the 
problem  can  be  stated  in  such  manner  that  either  one  variable  or  the 
other  can  be  made  the  independent  variable,  after  the  statement 
has  been  made  the  chart  should  be  consistently  drawn  so  that  the  inde- 
pendent variable  will  be  used  as  the  horizontal  scale  and  the  dependent 
variable  as  the  vertical  scale. 

As  Fig.  81  is  shown  it  is  necessary  for  the  person  interpreting  the 
chart  to  select  from  the  vertical  scale  some  number  of  feet  below 
the  surface  and  then  read  the  number  of  bacteria  per  cubic  centi- 
meter by  the  horizontal  distance  to  the  right.  It  is  only  after  some 
little  puzzling  that  the  reader  will  notice  that  the  scales  for  the 
variables  have  been  reversed  and  that  the  chart  has  been  practically 
turned  on  its  side.  How  this  chart  would  appear  if  the  horizontal 
scale  were  used  for  the  independent  variable  may  be  judged  by  turning 
the  book  and  looking  at  Fig.  81  from  the  left-hand  side  of  the  page. 
Though  it  is  easy  to  see  why  the  person  making  Fig.  81  happened  to 
arrange  the  chart  in  the  manner  shown  with  the  variables  reversed, 
the  gain  due  to  showing  depth  below  the  surface  in  the  vertical  direc- 
tion does  not  make  up  for  the  possibility  of  misinterpretation  which 
results  because  of  the  neglect  to  follow  standard  practice. 

In  Fig.  82  we  again  have  depth  plotted  downward  from  the  top 
of  the  chart.  As  we  wish  to  determine  the  velocity  of  the  stream  at 
different  depths  of  water,  depth  is  the  independent  variable  and 
velocity  is  the  dependent  variable.  The  arrangement  of  Fig.  82  is 
not  as  objectionable  as  Fig.  81,  for  the  upper  half  of  the  illustration 
shows  quite  clearly  in  pictorial  form  that  the  subject  under  considera- 
tion is  a  stream  having  a  channel  shaped  as  shown,  with  widths  and 
depths  as  indicated  by  the  two  scales.  In  the  bottom  portion  of  the 
diagram  the  scale  of  depths  downward  relates  very  definitelj^  to  the 
upper  portion  of  the  illustration  so  that  the  reader  cannot  easily  go 
astray.  Notice  that  the  curves  for  the  velocity  of  the  water  are  each 
plotted  on  a  separate  vertical  line  which  serves  as  zero  line.  The 
curves  for  velocity  begin  at  various  points  depending  upon  the  thick- 
ness of  the  ice,  as  will  be  seen  from  the  upper  portion  of  the  chart. 
There  is,  of  course,  no  velocity  in  that  portion  of  the  stream  which 


CURVE    PLOTTING 


87 


30 


Distances  in  feet 

40  50 

4, 


60 


70 


80 


90 


CURVES  OF  EQUAL  VELOCITY 


VERTICAL  VELOCITY  CURVES 
Note     Numbers  at  toiS  of  curves  indicate  measuring  points 
Numbers  at  bottom  of  curves  indicate  mean  velocity  m  the  vertical 


Horizontal  divisions  represent  one  foot  per  second  velocity 


Engineering  News 


Fig.  82.    The  Velocity  of  Water  in  Different  Portions  of  a  Stream  Flowing  under  Ice 

The  horizontal  scale  at  the  top  of  the  illustration  shows  points  where  velocity  measurements  were  made 
through  holes  in  the  ice.  Velocities  at  different  depths  are  indicated  by  the  curves  in  the  lower  half  of 
the  chart,  each  curve  being  plotted  to  the  right  of  a  vertical  zero  line  which  correspoiids  wdth  some  hole 
in  the  ice.  Lines  are  drawn  in  the  upper  portion  of  the  chart  showing  different  points  in  the  stream 
where  velocities  are  the  same 

is  frozen.  The  velocity  curves  end  abruptly  at  the  bottom  of  the 
stream.  It  will  be  seen  by  reading  velocities  horizontally  from  the 
different  zero  lines  from  which  the  curves  are  plotted  that  the  velocities 
are  considerably  greater  in  the  center  of  the  stream  than  they  are 
near  the  banks  or  the  bottom.  This  is  natural,  as  the  friction  of  the 
earth  bottom  and  sides,  as  well  as  the  friction  of  the  ice  at  the  top, 
causes  the  water  to  be  retarded  and  the  velocity  lessened.  In  the  upper 
portion  of  the  illustration  lines  are  drawn  through  all  those  points 
in  the  stream  cross-section  which  have  the  same  velocities.  The  lines 
are  similar  to  the  well-known  isothermal  lines  on  a  weather  map  show- 


88 


GRAPHIC    METHODS 


ing  where  the  temperatures  are  the  same.  From  these  Hnes  it  can  be 
seen  instantly  that  the  highest  velocity  is  at  the  center  of  the  stream, 
as  far  away  as  possible  from  retarding  influences.  Velocities  gradually 
grow  less  as  the  sides,  the  bottom,  or  the  ice  at  the  top  are  approached. 


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Courtesy  of  Data.  Chicago 

Fig.  83.    Relative  Value  of  Different  Coals  as  Compared  to  Anthracite  Coal 

The  price  of  anthracite  coal  is  here  the  "  independenti  variable  "  since  it  is  the  standard  or  measure  by  which 
the  other  variable  is  judged.  The  price  of  anthracite  coal  should  have  been  made  the  horizontal  scale 
of  the  chart.     See  Fig.  84 

Fig.  82  is  an  interesting  piece  of  work  and  the  method  used  in  charting 
is  justifiable,  even  though  in  this  case,  as  in  the  preceding,  the 
independent  variable  is  plotted  downward  and  the  dependent  variable 
is  plotted  horizontally. 


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Price  of  Anthracite  Coal  —  Dollars 


10 


It 


Fig.  84.    Relative  Value  of  Different  Coals  as  Compared  to  Anthracite  Coal 

With  the  arrangement  sho-mi  here  the  curve  lines  for  different  coals  appear  in  their  correct  position.  Illinois 
coal  is  at  the  bottom  instead  of  at  the  top.  The  heavy  line  here  drawn  for  anthracite  proves  at  a  glance 
which  fuels  are  better  and  which  poorer  than  anthracite 


CURVE    PLOTTING  89 

Fig.  83  is  intended  as  a  comparison  between  different  kinds  of 
coal  from  the  standpoint  of  actual  heating  value.  At  the  first  glance 
at  this  chart  the  reader  sees  that  the  line  for  Illinois  coal  is  above  the 
other  lines,  and  he  is  apt  to  draw  the  conclusion  that  Illinois  coal  is 
better  than  anthracite,  coke,  or  Pocahontas  coal.  It  is  only  after 
some  puzzling  over  the  chart  that  one  notices  that  the  whole  chart 
has  been  drawn  in  reversed  order.  We  are  considering  what  the 
relative  values  of  other  coals  may  be  if  we  know  the  value  of  anthracite 
coal.  The  whole  scheme  of  reasoning  begins  with  the  "price  of  an- 
thracite coal."  The  "price  of  anthracite  coal"  is  the  independent 
variable  and  should  be  plotted  horizontally,  with  the  "relative  value 
in  dollars"  plotted  as  the  vertical  scale.  The  reader  may  get  a  correct 
impression  of  the  chart  in  Fig.  83  if  he  will  turn  over  the  page  and 
read  the  chart  by  holding  the  page  up  to  the  light  in  such  manner 
that  the  zeros  of  the  two  scales  appear  at  the  lower  left-hand  corner. 
When  this  is  done,  it  will  be  seen  that  the  relative  value  of  Pocahontas 
coal  exceeds  each  of  the  other  fuels  mentioned  and  that  Illinois  coal 
comes  not  at  the  top  of  the  list,  but  at  the  bottom  of  the  list  in  so  far 
as  fuel  value  is  concerned. 

Fig.  84  has  been  drawn  with  the  "price  of  anthracite  coal"  as  the 
horizontal  scale,  where  it  belongs  because  it  is  the  independent  vari- 
able. The  lines  for  different  fuels  now  appear  in  their  correct  order, 
and  the  reader  sees  at  a  glance  that  Pocahontas  coal  has  more  fuel 
value  than  anthracite  coal.  Notice  that  a  heavy  line  has  been  used 
for  the  curve  line  drawn  for  anthracite  coal.  As  this  line  is  the  standard 
by  which  the  values  are  compared,  it  seems  best  to  give  it  prominence 
on  the  chart.  The  position  of  other  curve  lines  above  or  below  this 
line  shows  instantly  whether  the  fuels  are  better  or  worse  than  anthra- 
cite in  relative  value. 

In  Fig.  85  an  effort  has  been  made  to  show  detail  time-studies 
by  the  use  of  curves.  There  is  an  error  here,  however,  in  that  the  curve 
has  been  arranged  in  such  manner  that  the  independent  variable  is 
drawn  vertically  and  the  information  desired  as  "time  in  seconds" 
must  be  read  off  from  the  horizontal  scale.  The  reader  wishes  to 
know  how  many  seconds  are  required  for  any  one  step  or  any  series 
of  steps  in  the  whole  work.  The  chart  can  be  interpreted  in  the  accus- 
tomed way  if  the  page  is  turned  over,  and  the  diagram  read  by  hold- 
ing the  page  in  such  manner  that  the  zero  on  the  scale  of  "time  in 
seconds"  appears  at  the  lower  left-hand  corner  of  the  chart  when  the 


90 


GRAPHIC    METHODS 


page  is  held  up  toward  a  light.  The  curve  for  operator  No.  1  then 
appears  below  the  curve  for  operator  No.  2  and  the  chart  shows  cor- 
rectly  the   relative   merits    of   the   two   operators.     Fig.  86  is  a    re^ 

drawing  of  the  data 
shown  in  Fig.  85. 
Here  the  curves  for 
the  two  operators 
appear  in  their  cor- 
rect relative  position, 
and  it  is  seen  at  once 
that  operator  No.  1 
is  the  more  rapid 
worker,  since  he  uses 
less  time.  With  the 
independent  vari- 
able made  the  hori- 
zontal scale,  a  chart 
can  be  interpreted 
quickly.  If  the  de- 
pendent variable  is 
used  as  the  horizon- 
tal scale  the  reader  is 
likely  to  draw  a  con- 
clusion the  reverse  of 
that  the  chart  was 
intended  to  show. 


Operator  No.l.             Ocerator  No.  2 

smoothes                       _                                   i           -? 

label                --                 -                                          r 

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Time   in    seconds 


Fig.  85.    Record    of    a    Detailed    Time-ScUuy  of    'iv\o 
Operators  Labeling  Packages 

We  are  here  studying  the  time  for  different  operations.  The  names  of 
the  operations  constitute  the  independent  variable  while  time  is 
the  dependent  variable.  The  chart  reverses  the  proper  arrangement 
of  scales  and  causes  the  curve  for  operator  No.  1  to  appear  improperly 
above  the  curve  for  operator  No.  2.     Compare  Fig.  86 


Fig.  87  shows  the  data  of  Fig.  85  and  Fig.  86  redrawn  in  the  form 
of  horizontal  bars  such  as  were  seen  in  Chapter  I  and  Chapter  II. 
The  relative  times  for  the  various  operations  are  shown  much  more 
clearly  b}^  the  horizontal  bars  than  by  the  curves  used  in  Fig.  85  and 
Fig.  86.  The  time  in  seconds  required  for  each  operation  is  given 
by  detailed  dimension  lines  above  each  section  in  the  horizontal  bar, 
and  the  comparative  total  time  of  the  two  different  men  can  also  be 
grasped  instantly.  The  total  time  in  seconds  for  the  whole  series 
of  operations  is  shown  by  an  over-all  dimension  line  above  each  of 
the  bars,  and  the  reader,  if  he  wishes,  may  make  an  accurate  com- 
parison between  operator  No.  1  and  operator  No.  2  by  using  a  numerical 
ratio.  A  chart  of  this  kind  can  be  very  quickly  made  for  ordinary 
office  purposes  if  the  horizontal  bars  are  drawn  on  co-ordinate  paper 


CURVE    PLOTTING 


91 


and  the  different  areas  made  to 
stand  out  in  contrast  by  the  use  of 
colored  crayons.  The  actual  differ- 
ences between  the  two  operators 
would  show  more  clearly,  operation 
by  operation,  if  lines  were  used  join- 
ing the  ends  of  the  components  in 
the  two  bars  in  a  manner  similar  to 
that  seen  in  Fig.  32.  The  data  of 
Fig.  85  do  not  lend  themselves  well 
to  presentation  in  curve  form.  In 
Fig.  85  and  in  Fig.  8G  the  shape 
of  the  curves  means  nothing,  since 
there  is  no  numerical  scale  relating 
to  the  names  of  operations.  Fig. 
87  shows  a  much  more  satisfactory 
method  for  portraying  the  data. 

In  Fig.  88  we  have  an  applica- 
tion of  curves  to  advertising  in  pop- 
ular magazines.  The  curves  de- 
pict the  circulation  of  a  newspaper, 


50 

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35 
30 
25 
20 
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label  with 

glue 

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label  on 
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Operations 

Fig.  86.  Record  of  a  Detailed  Time- 
Study  of  Two  Operators  Labeling 
Packages 

Here  the  scales  have  been  properly  arranged  and 
the  two  curves  appear  in  their  correct  relative 
position  on  the  chart.  These  data,  however, 
are  not  well  suited  for  curve  presentation 
and  they  are  more  clearly  brought  out  by  the 
bar  method  used  in  Fig.  87 


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Fig.  87.    Record  of  a  Detailed  Time-Study  of  Two  Operators  Labeling  Packages 

By  this  method  of  presentation  the  reader  may  see  clearly  the  relative  'ength  of  time  for  different  operations 
as  well  as  the  comparison  of  total  time  taken  by  the  two  workers.  Dimension  marks  and  figures  show 
conveniently  the  actual  number  of  seconds  required.  The  different  operations  have  here  been  given 
numbers  instead  of  names.     The  scale  to  which  the  chart  is  drawn  is  named 


1905         1906 


GRAPHIC    METHODS 
1907  1908         1909  1910 


1911 


1912 


1913 


100.000 


The  Plain  Dealer's  circulation  Is  by  far  the 
largest  net  paid  morning;  and  Sunday  newspaper 
circulation  between  New  York  and  Chicago:  and 
in  Cleveland  and  the  retail  trading  area  tributary 
to  Cleveland — a  radius  of  75  miles  at  most-  the 
Plain  Dealer's  net  paid  circulation  is  double  the 
net  paid  circulation  of  any  other  Cleveland 
morning  or  Sunday  newspaper.  Every  record 
bearing  directly  or  indirectly  upon  figures  above 
published  or  upon  any  other  detail  of  Plain 
Dealer  Circulation  or  Advertising  is  open  to  the 
most  complete  and  searching  investigation  to 
anyone  at  any  time  and  without  further  notice. 


ffiit 


'4^vn 


ir_ 


Etitfr  £i 


m- 


150000 


10000 


I0O.00O 


70000 

EXPLANATION  OF  CHART 

This  chart  shows  the  Cleveland  Pleiin  Dealer's  circulation  by 
months  from  February  1905  to  June  1913.  Elach  line  up  and  down 
represents  a  month,  each  line  across  a.  thousand  copies  sold.  Note 
how  the  top  line  indicating  Sunday  sales,  and  the  lower  line  indi- 
cating daily  sales  move  steadily  upward:  Observe  the  steady, 
healthy,  sturdy  grovvth  from  the  first  month  to  the  last — no  sudden 
mushroom-like  gains,  no  unexplained  losses,  but  a  consistently 
increasing  total  affected  only  by  the  changing  seasons  and  the  bus^ 
iness  health  of  the  whole  country. 

Cleveland  Plain  Dealer 

Fig.  88.    The  Use  of  Curves  in  an  Advertisement  to  Show  the  Growth  in  Circulation 

of  a  Newspaper 

It  is  unfortunate  that  this  iUustration  was  not  made  so  as  to  show  the  zero  line  of  the  vertical  scale.  In 
advertising  work  it  usually  pays  to  avoid  anything  which  might  seem  like  exaggeration.  Omitting 
the  zero  line  makes  the  growth  seem  more  rapid  than  it  would  if  the  zero  line  were  included  in  a  chart 
drawn  to  scale.  Though  the  drafting  on  this  chart  might  have  been  better,  the  application  of  curves  to 
advertising  deserves  commendation 

with  the  object  of  convincing  advertising  managers  that  this  par- 
ticular newspaper  is  a  desirable  one  in  which  to  place  advertisements 
because  of  the  rapidly  and  steadily  increasing  circulation.  It  is  sur- 
prising that  circulation  managers  of  newspapers  have  not  more  often 
used  charts  to  show  circulation,  instead  of  the  wordy  typed  state- 
ments so  frequently  seen  claiming  great  growths  in  circulation  over 
a  period  of  months  or  years.  Though  Fig.  88  shows  a  commendable 
progressiveness  on  the  part  of  this  particular  ncAvspaper  in  adapting 
curves  to  circulation  statements,  it  seems  necessary  to  point  out  the 
fact  that  the  chart  may  cause  distrust  in  the  minds  of  some  readers. 
There  is  a  chance  that  the  man  who  has  advertising  to  place  may  feel 


CURVE    PLOTTING 


93 


that  the  chart  has  been  drawn  in  too  optimistic  a  manner  because  it 
does  not  show  zero  at  the  bottom  of  the  scale.  It  wotild  have  given 
a  much  more  conservative  impression  if  the  excellent  record  of  circu- 
lation growth  had  been  plotted  in  curves  having  the  zero  line  shown 
at  the  bottom  of  the  chart,  so  that  the  relative  growth  could  be  accu- 
rately judged  visually. 

In  Fig.  89  a  large  amount  of  information  has  been  condensed  into 
a  small  amount  of  space,  yet  the  chart  is  fairly  clear  and  easy  of  in- 
terpretation. Several  ingenious  combinations  have  been  included  as, 
for  instance,  the  arrows  that  show  the  prevailing  direction  of  the 
wind  each  day.  The  chart  gives  unusually  complete  information  in 
a  most  convenient  form  for  any  ventilating  engineer  or  power-plant 
manager  who  wishes  to  keep  careful  track  of  his  cost  of  coal  in  different 
months  of  the  year  as  dependent  upon  weather  conditions. 


DAY  OF  MONTH 


Heating  aTid  Ventilating  Magazine 

Fig.  89.    Record  of  the  Weather  in  New  York  City  for  December,  1912 

The  heavy  line  indicates  temperature  in  degrees  Fahrenheit 
The  light  solid  line  shows  wind  velocity  in  miles  per  hour 

The  dotted  line  depicts  relative  humidity  in  percentage  from  readings  taken  at  8  a.m.  and  8  p.m. 
Arrows  portray  the  prevailing  direction  of  the  wind 

Initials  at  the  base  of  the  chart  show  weather  conditions  as  follows:     S,  clear;  PC,  partly  cloudy;  C,  Cloudy; 
R,  rain;  Sn,  snow 

Fig.  90  shows  an  example  of  double  co-ordinate  ruling  on  the 
same  sheet  of  paper.  The  scheme  of  using  double  co-ordinates  is 
not  very  well  known  even  to  engineers  and  it  seems  worthy  of  atten- 
tion here.  The  solid  line  plotted  in  the  general  form  of  a  curve  with 
a  flat  space  for  each  month  shows  the  total  water  consumption  in 
millions  of  gallons  per  day.  The  total  water  consumption  is  read 
from  the  scale  of  the  horizontal  lines  as  for  any  curve  plotted  by 
rectangular  co-ordinates.    The  slanting  lines  are  drawn  after  the  total 


94  GRAPHIC    METHODS 

number  of  gallons  used  per  day  has  been  divided  by  the  number  of 
inhabitants  in  the  district  so  as  to  obtain  a  figure  for  the  average 
daily  consumption  of  water  j)er  capita.  As  the  population  figure  used 
depends  upon  census  records  it  may  be  necessary  to  get  the  rate  of 
growth  in  the  population  from  records  as  much  as  ten  years  apart. 
In  Fig.  90  it  can  be  observed  that  the  slanting  lines  showing  the  rate 
of  growth  of  the  city  are  straight  lines,  indicating  probably  that  the 
census  figures  were  used  in  the  drawing  of  these  lines  because  yearly 
figures  could  not  be  obtained.  If  yearly  figures  were  obtainable  the 
slanting  lines  could  be  extended  year  by  year  until  they  reached 
completely  across  the  chart.  The  rate  of  growth  in  population  deter- 
mines the  angle  of  the  slanting  lines,  the  more  rapid  the  growth  the 
greater  the  angle  of  the  lines. 

The  slanting  lines  are  located  on  the  page  so  that  a  curve  can  be 
read  from  either  the  horizontal  lines  or  from  the  slanting  lines.  The 
method  of  locating  the  slanting  lines  can  be  worked  out  by  anyone 
who  will  experiment  a  little  in  making  a  chart  of  this  type.  When  the 
population  is  known  and  the  total  consumption  is  known,  it  is  only  a 
matter  of  division  to  determine  the  consumption  'per  capita.  After  the 
slanting  lines  are  once  placed  upon  the  chart,  the  curve  can  be  read 
either  from  the  horizontal  lines  showing  the  total  consumption  or 
from  the  slanting  lines  showing  gallons  per  capita. 

Taking  the  peak  for  February,  1912,  we  see  that  the  total  con- 
sumption averages  during  the  month  142,000,000  gallons  per  day. 
Reading  this  same  month  from  the  slanting  lines  we  observe  that  the 
average  consumption  per  capita  daily  was  127  gallons.  Notice,  that 
while  the  total  consumption  in  gallons  was  much  larger  in  February, 
1912,  than  in  January,  1909,  as  seen  by  considering  the  horizontal 
lines,  the  consumption  per  capita  in  February,  1912,  read  from  the 
slanting  lines,  was  somewhat  less  than  in  January,  1909. 

If  we  consider  the  growth  in  the  population  of  the  city  of  Boston, 
it  is  permissible  that  the  total  water  consumption  in  1912  should  be 
greater  than  in  1908.  In  spite  of  the  large  growth  of  the  city  from; 
1908  to  1912,  there  has  been  a  general  decrease  in  the  total  quantity 
of  water  consumed.  The  decrease  in  total  consumption  is  chiefly 
due  to  the  metering  of  water  to  individual  users,  eliminating  a  larg( 
part  of  the  water  waste  which  formerly  occurred  because  of  careless-' 
ness  on  the  part  of  consumers.  The  actual  percentages  of  the  services 
which  were  metered  in  each  one  of  the  years  considered  may  be  seen 


CURVE    PLOTTING 


95 


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Courlesn  of  Hazen  &  Whipple,  Xew  York. 

Fig.  go.  Chart  Showing  by  Months  the  Average  Total  Daily  Water  Consumption  in 
Boston,  and  by  Months  the  Average  Daily  per  Capita  Water  Consumption.  Also 
the  Yearly  Average  of  Daily  Consumption  Stated  in  Total  and  per  Capita 

In  this  illustration  the  curves  may  be  read  from  either  of  two  different  sets  of  co-ordinate  rulings.  Using 
the  horizontal  ruled  lines,  we  may  read  from  the  curves  the  average  total  consumption  per  day.  By 
reading  from  the  slanting  lines,  the  same  curves  may  be  interpreted  as  the  average  consumption  per 
capita  per  day.  The  scheme  of  using  two  sets  of  co-ordinate  rulings  is  a  valuable  one.  The  scale  for 
"million  gallons  per  day"  should,  however,  have  been  shown  only  at  the  left,  with  the  slanting  line 
scale  for  "gallons  per  capita"  placed  in  the  right-hand  margin  for  the  sake  of  clearness 

by  referring  to  the  figures  near  the  upper  portion  of  the  chart.  Note 
that  in  1908,  21  per  cent  of  the  services  were  metered,  while  in  1911, 
45  per  cent  were  metered.  The  proportion  of  the  services  metered  in 
1912  was  not  known  at  the  time  the  chart  was  made  and  hence  is 
not  recorded. 

A  httle  study  of  Fig.  90  will  show  that  there  is  a  very  striking 
similarity  in  the  shape  of  the  waves  for  different  calendar  years.  Water 
consumption  is  high  in  the  winter  and  again  high  in  the  summer  months, 
with  the  lowest  point  each  year  usually  found  in  November.  The 
exact  amount  of  resemblance  of  these  waves  to  each  other  could  be 
determined  in  an  interesting  manner  if  a  separate  curve  were  plotted 
for  each  year  so  that  all  the  curves  would  be  shown  one  above  the 
other  in  the  manner  seen  in  Fig.  103. 


I 


96'  GRAPHIC    METHODS 

1. 

Just  how  much  the  total  consumption  in  water  has  been  decreased, 
even  though  there  was  an  increasing  population,  may  be  seen  by  re- 
ferring to  the  dotted  line  on  the  chart.  This  dotted  line  was  plotted 
from  points  which  represent  the  average  for  the  whole  of  each  year. 
Thus,  the  average  in  1905  was  about  122  million  gallons  per  day  and 
in  1911  about  113  million  gallons  per  day.  There  is  so  great  a  fluc- 
tuation in  the  main  curve  from  month  to  month  that  it  would  be  diffi- 
cult to  judge  accurately  whether  the  average  consumption  is  going 
up  or  down  if  some  such  curve  as  the  dotted  line  were  not  used.  An 
average  curve  line  run  through  a  curve  in  the  manner  shown  by  the 
dotted  line  in  Fig.  90  is  of  great  assistance  in  drawing  accurate  con- 
clusions from  curves  which  have  much  fluctuation. 

In  Fig.  90,  the  dotted  line,  plotted  through  a  point  giving  the 
average  for  each  year,  thoroughly  eliminates  all  the  fluctuations 
which  would  be  so  confusing  to  the  reader  if  he  had  to  study  only  the 
monthly  curve.  The  dotted  line  shows  conclusively  by  its  slant  that 
the  total  consumption  from  1905  to  1908  inclusive  went  up  just  about  \ 
as  rapidly  as  the  growth  of  the  population  would  lead  one  to  expect. 
After  1908,  however,  there  was  a  tremendous  drop  in  total  consump- 
tion, even  though  the  population  kept  on  increasing.  In  1912,  the 
average  total  consumption  per  day  went  up  somewhat  above  1911, 
but  yet  it  did  not  increase  much  more  rapidly  than  the  slanting  line 
of  the  per  capita  scale  might  indicate  as  permissible.  Fig.  90  could 
have  been  improved  somewhat  if  the  dotted  line  had  been  replaced 
by  a  broad  black  line  which  would  bring  the  yearly-average  curve 
vividly  to  the  attention  of  the  reader.  The  yearly-average  curve 
really  gives  the  most  interesting  conclusions  which  can  be  drawn 
from  this  chart  and  it  is  worthy  of  greater  emphasis  to  the  eye  than 
is  given  to  it  in  the  chart. 

It  would  have  been  better  if  the  scale  for  "millions  of  gallons  per 
day"  had  been  placed  only  at  the  left-hand  edge  of  the  chart  in  heavy 
lettering  so  the  figures  would  stand  out  clearly.  The  scale  for  the 
slanting  co-ordinate  lines  could  then  be  placed  at  the  end  of  each 
slanting  line  at  the  right-hand  side  of  the  chart.  The  scale  for  the 
slanting  co-ordinate  lines  is  too  difficult  to  find  in  Fig.  90. 

An  interesting  study  could  be  made  from  Fig.  90  by  plotting  a 
curve  which  would  show  each  year  the  percentage  of  services  which 
were  not  metered,  instead  of  using  the  figures  at  the  top  of  the  chart 
which  show  the  percentage  of  services  which  are  metered.     A  curve 


CURVE    PLOTTING  97 

for  the  percentages  of  services  not  metered  should  show  some  similarity 
in  shape  to  the  dotted  line  curve  in  Fig.  90,  giving  the  yearly  average 
of  daily  consumption. 

When  any  curve  fluctuates  greatly,  the  general  trend  of  the  curve 
can  be  most  easily  determined  if  the  method  of  moving  averages  is 
used.  If  data  are  plotted  by  months,  a  moving  average  is  frequently 
made  to  include  twelve  months.  As  a  succeeding  month  is  included 
in  the  moving  average,  that  calendar  month  of  the  preceding  year  is 
dropped  out  of  the  average  so  that  the  average  always  includes  twelve 
months.  The  moving-average  curve  is  a  much  smoother  curve  than 
a  curve  made  from  the  monthly  figures,  and  is  accordingly  more  easily 
interpreted.  The  degree  of  smoothness  of  any  moving-average  curve 
depends  chiefly  on  the  number  of  points  included  in  the  moving  av- 
erage as  compared  with  the  number  of  points  in  one  complete  wave 
or  cycle  in  the  data  curve,  and  the  moving-average  curve  is  most 
smooth  if  the  moving  average  includes  the  same  number  of  points 
as  are  usually  found  in  one  complete  wave  or  cycle  of  the  fluctuating 
curve. 

Many  curves  plotted  by  weekly  or  monthly  observations  show  a 
complete  wave  or  cycle  each  year  because  of  the  effect  of  the  seasons. 
With  such  a  curve  it  is  best  to  use  for  the  moving  average  the  number 
of  points  included  in  one  year  of  the  fluctuating  curve.  When,  how- 
ever, we  study  curves  relating  to  financial  conditions  in  any  country, 
we  find  that  there  are  complex  cycles  which  involve  several  years. 
With  such  a  complex  curve  considerable  care  must  be  used  to  deter- 
mine the  average  length  of  one  wave  or  cycle,  so  that  the  moving- 
average  curve  may  be  made  as  smooth  as  possible  and  most  nearly 
represent  the  data  being  studied. 

In  Fig.  91  the  data  when  plotted  by  years  give  such  a  complex 
curve  that  it  is  not  easy  to  determine  just  how  rapidly  exports  have  in- 
creased. To  show  the  effect  of  different  numbers  of  points  included 
in  a  moving  average,  curves  were  drawn  with  moving  averages  for 
three  years,  five  years,  and  ten  years.  Since  the  distance  between 
peaks  on  the  curve  making  one  cycle  of  fluctuation  averages  more 
nearly  ten  years  than  three  years  or  five  years,  the  ten-year  curve 
more  closely  approximates  a  smooth  curve  line  than  either  of  the 
other  two  curves.  As  a  matter  of  fact,  the  intervals  between  peaks 
change  somewhat  so  that  it  is  difficult  to  select  any  one  number  of 
years  as  the  correct  number  for  use  in  making  up  the  moving  average. 


98 


GRAPHIC    METHODS 


CURVE    PLOTTING  99 

The  heavy  smooth  curve  was  drawn  finally  by  using  the  points  which 
represent  the  averages  of  the  decades  and  then  sketching  in,  free 
hand,  a  line  which  gives  a  smooth  curve  and  removes  the  waves  found 
in  the  ten-year  moving-average  curve.  Notice  that  the  heavy  smooth 
curve  is  so  drawn  through  the  ten-year  curve  as  to  give  approximately 
equal  areas  on  either  side  of  the  smooth  curve  between  that  curve 
and  the  curve  for  the  ten-year  moving  average.  The  curve  for  the 
ten -year  moving  average  evidently  does  not  give  a  fair  interpretation 
of  yearly  data,  because  the  ten-year  average  curve  shows  a  peak  in 
the  year  1886  while  the  data  as  plotted  by  years  show  a  valley  for  that 
year.  The  peak  in  the  ten-year  moving-average  curve  in  1886  was 
caused  by  the  number  of  years  included  in  the  moving  average  not 
being  a  true  representation  of  the  length  of  one  full  cycle.  The  length 
of  the  cycle  changes  from  time  to  time,  so  that  no  one  selected  cycle 
length  is  satisfactory  for  the  whole  curve.  The  heav}^  curve  sketched 
in  by  hand  is  the  fairest  approximation  to  show  the  trend  of  the  fluc- 
tuating curve  as  a  whole. 

In  Fig.  91  the  points  on  any  smoothed  curve  are  plotted  midway 
horizontally  in  the  range  of  years  included  in  each  moving  average. 
It  is  on  this  account  that  the  smoothed  curves,  though  all  plotted 
from  the  same  data,  do  not  seem  to  end  at  the  same  year  at  the  right- 
hand  side  of  the  chart.  Though  it  is  good  practice  to  plot  smoothed 
curves  in  this  manner  with  each  point  midway  in  the  horizontal  range 
of  the  points  included  in  any  moving  average,  there  are  times  when 
it  is  not  desirable  to  have  the  point  on  the  moving-average  curve  fall 
behind  the  latest  point  on  the  data  curve.  For  operating  records  in 
industrial  work,  the  moving-average  curve  is  convenient  to  show  an 
average  for  the  preceding  twelve  months  or  for  any  other  length  of 
time  immediately  preceding.  With  such  curves  it  is  usually  best  to 
have  the  last  point  of  the  moving-average  curve  plotted  on  the  same 
vertical  co-ordinate  line  as  the  last  point  of  the  data  curve. 

Index  numbers  are  used  very  commonly  in  the  study  of  facts 
relating  to  the  prices  of  commodities  over  a  long  period  of  time.  When 
making  comparisons  by  index  numbers,  conditions  are  selected  which 
as  nearly  as  possible  represent  the  normal  or  typical  conditions  for  the 
subject  under  consideration.  The  figures  for  other  dates  are  then 
compared  with  the  figures  representing  the  normal  conditions,  by  work- 
ing on  a  percentage  basis  so  that  the  figures  for  the  normal  conditions 
are  taken  as  unity  or  100  per  cent.    Figures  for  the  conditions  to  be 


100 


GRAPHIC    METHODS 


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compared  with  the  normal  are  expressed  in  percentages,  making  the 
increases  above  normal  in  figures  above  100  per  cent  and  decreases 
below  normal  in  figures  below  100  per  cent.  Unfortunately,  the  reader 
not  familiar  with  index  numbers  may  not  realize  that  a  chart  relating 
to  index  numbers  should  be  read  from  the  100  per  cent  line  rather 
than  from  the  base  of  the  chart.  It  is  very  common  to  find  a  chart 
relating  to  index  numbers  so  drawn  that  the  chart  does  not  extend 
to  the  zero  of  the 
vertical  scale.  Such 
a  chart  may  give  a 
false  impression  of 
much  more  violent 
fluctuation  than 
would  be  interpreted 
from  a  chart  plotted 
on  the  usual  co-or- 
dinate field  and 
showing  the  zero  of 
the  vertical  scale. 

Fig.  92  is  taken 
from  the  United 
States  Government 
Crop  Reporter,  a 
magazine  widely  dis- 
tributed to  farmers. 
It  has  been  the  hope  of  this  magazine  to  give  producers  of  agricultural 
products  an  opportunity  to  study  the  price  records  of  previous  years,  so 
that  they  may,  in  so  far  as  possible,  sell  at  the  time  of  the  year  when 
prices  are  the  highest.  It  is  much  to  be  doubted  whether  the  average 
reader  of  charts  like  that  seen  in  Fig.  92  would  realize  that  the  100  per 
cent  line  must' be  used  as  a  basis  for  interpreting  the  chart.  The  100  per 
cent  line  has  not  been  made  any  heavier  than  the  other  lines  on  the 
sheet.  A  man  who  had  been  at  all  accustomed  to  reading  charts 
having  zero  at  the  base  of  the  chart  would  be  apt  to  read  Fig.  92  as 
though  the  bottom  line  were  the  zero  from  which  the  curve  had  been 
drawn.  On  such  a  basis,  he  might  think  that  the  price  of  eggs  in 
January,  1912,  was  more  than  eight  times  the  price  in  July,  1911. 
Such  a  conclusion  would,  of  course,  be  entirely  unwarranted  by  the 
actual  figures. 


United  Statcs\Governmcnl  Crop  Reporter 

Fig.  92.  Fluctuation  in  the  Price  of  Eggs  in  the  United 
States  as  Compared  with  the  Average  of  the  Monthly 
Figures  for  the  Preceding  Four  Years 

An  untrained  reader  may  not  realize  that  this  chart  must  be  read  from 
the  line  representing  100  per  cent.  Charts  for  index  numbers,  where 
the  fluctuation  is  compared  with  100  per  cent,  should  have  the  100 
per  cent  line  made  broad,  and  a  wavy  line  should  be  used  at  the 
bottom  of  the  chart  unless  the  zero  of  the  scale  is  shown.  An  alter- 
native arrangement  is  shown  in  Fig.  93 


CURVE    PLOTTING 


idi 


Where  charts  for  index  numbers  are  made  on  the  100  per  cent 
basis,  it  would  seem  best  to  have  a  broad  hne  for  the  100  per  cent 
hue.  If  there  is  not  room  to  extend  the  co-ordinate  field  down  to  the 
zero  of  the  vertical  scale,  the  co-ordinate  field  may  be  shown  broken 
ott  with  a  wavy  line  at  the  base  indicating  to  the  reader  that  the  bot- 
tom of  the  chart  is  not  a  zero  line,  and  that  the  chart  must  be  read  on 
the  100  per  cent  basis. 

Fig.  93  was  drawn  from  the  data  of  Fig.  92  as  a  suggestion  for  a 
type  of  chart  which  might  be  used  where  an  untrained  class  of  readers 
must  be  reached.  By  plotting  increases  above  the  zero  line  and  de- 
creases below  the 
zero  line,  a  chart 
is  obtained  which 
needs  little  space 
and  which  never- 
theless is  on  a  large 
scale,  giving  a 
great  amount  of 
detail  so  as  to  per- 
mit accurate  read- 
ing of  all  the  vari- 
ous points  on  the 
curve.  There  is 
very  small  chance 
for  any  untrained 
reader  to  misin- 
terpret a  chart 
made  by  the  gen- 
eral method  used 
in  Fig.  93. 

Fig.  94  is  essentially  a  chart  relating  to  index  numbers.  The 
vertical  scale,  instead  of  being  shown  with  100  per  cent  to  represent 
unity,  has  zero  placed  opposite  the  line  representing  unity.  The  chart 
does  not  clearly  point  out  that  the  curve  drawn  above  the  zero  or 
unity  line  represents  increases  in  revenues  and  not  total  revenues. 
A  much  greater  fault  with  the  chart,  however,  is  found  in  the  fact 
that  the  chart  compares  the  operation  of  a  railroad  in  different  years 
by  using  the  year  1908  as  unity.  1908  was  a  panic  year,  with  very 
serious  business  depression  affecting  railroads  even  more  than  some 


Fig.  93.  Fluctuation  in  the  Price  of  Eggs  in  the  United 
States  as  Compared  with  the  Average  of  the  Monthly- 
Figures  for  the  Preceding  Four  Years 

The  Government  Crop  Reporter  is  intended  to  be  of  service  to  farmers. 
Any  charts  included  should  be  as  clear  as  it  is  possible  to  make  them. 
The  illustration  above  is  submitted  only  as  a  suggestion 


10£* 


GRAPHIC    METHODS 


1910 


19/f 


might 
from 


of  the  industrial  companies.  All  the  years  following  1908  are  likely 
to  show  a  greatly  increased  volume  of  business  in  practically  any  field 
of  commerce  or  industry.  Because  1908  was  selected  as  unity  in  Fig. 
94,  the  reader  would  be  justified  in  feeling  that  the  increased  amount 

of  revenue  in  the  years 
following  1908 
have  come  solely 
the  improvement  in 
general  business  condi- 
tions, without  any  as- 
sistance whatever  from 
ability  in  managing  the 
railroad.  If  the  better- 
ment in  the  general 
prosperity  of  the  coun- 
try were  great  enough, 
it  might  even  be  pos- 
sible to  show  in  Fig.  94 
a  large  increase  in  oper- 
ating revenue  due  only 
to  the  general  improve- 
ment in  business  con- 
ditions and  in  spite  of 
reduced  efficiency  in 
the    operation    of    this 

reader's  mind  whether  the  better  showing  of  the  railroad  is  due  to    ] «  f]  | t^ J fl ,  i  o  1  ra  i  1  roa  d     COn  - 


Annual  Report  of  the  Wheeling  and  Lake  Erie  Railroad,  1912 

Fig.  94.  Improvement  in  Economy  of  Operation  of 
the  Wheeling  and  Lake  Erie  Raihroad,  1908  to  1912 

It  will  be  noticed  from  the  upper  left-hand  corner  of  the  chart  that 
the  year  1908  is  taken  as  unity.  1908  was  a  year  of  great  business 
depression.  As  business  conditions  naturally  improved  in  the 
years  following  1908,  there  could  be  a  legitimate  question  in  the 


better  management  or  to  the  increase  in  the  general  prosperity 
of  the  country 


sidered  "per  se.  It  is 
not  intended  here  to  cast  any  reflections  upon  the  managing  ability 
on  the  railroad  in  question.  The  only  object  in  mentioning  the  matter 
at  all  is  to  point  out  the  fact  that  the  use  of  the  year  1908  as  unity 
puts  the  road  unnecessarily  under  suspicion  of  attempting  to  mislead 
the  public. 

In  any  chart  where  index  numbers  are  used  the  greatest  care 
should  be  taken  to  select  as  unity  a  set  of  conditions  thoroughly  typical 
and  representative.  It  is  frequently  best  to  take  as  unity  the  average 
of  a  series  of  years  immediately  preceding  the  years  for  which  a  study 
is  to  be  made.  The  series  of  years  averaged  to  represent  unity  should, 
if  possible,  be  so  selected  that  they  will  include  one  full  cycle  or  wave 
of  fluctuation.     If  one  complete  cycle  involves  too  many  years,  then 


CURVE    PLOTTING 


103 


the  years  selected  as  unity  should  be  taken  in  equal  number  on  either 
side  of  a  year  which  represents  most  nearly  the  normal  condition. 

Fig.  95  is  an  illustration  reduced  in  size  from  a  large  chart  10  by  14 
inches.  The  chart  is  of  especial  interest  because  it  is  one  of  a  series 
of  several  hundred  charts  submitted  to  the  board  of  arbitration  in 
the  concerted  wage  movement  in  the  eastern  territory  by  the  Order 
of  Railroad  Conductors  and  Brotherhood  of  Railroad  Trainmen  in 
1913.  These  charts  cover  practically  all  phases  of  railroad  operation 
and  give  in  condensed  form  a  tremendous  quantity  of  information. 

RELATIVE  RETAIL  PRICES  OF  FOOD:  SIMPLE  AND  WEIGHTED  AVERAGES-UNITED  STATES 


1890- 

1912 

AVERASE    RBICE    FOR    1890-1689=    lOO.O 

1690      1891      1892     1893     1894      1895      1896      1897      1898      1899      1900     1901     1902      1903     1904      190S     1906     1901      1808      1909     1910      1911      19 

12 

Simple 
Year         Average 

1 

RelatlTe 

Prloee 

/ 

890  102.0 

891  103.6 

892  101.7 

893  104. « 

894  99.6 

895  97.2 

896  94.9 

897  96.4 

898  99.4 
699              100.6 

900  102.9 

901  109.5 

902  116.8 

903  116.9 

904  118.3 
90B               118.3 

906  122.4 

907  128.0 

908  132.5 

909  140.3 

910  143.5 

911  146.9 

101. 
103. 
101. 
104. 

99. 

97. 

96. 

96. 

99. 
100. 
103. 
108. 
114. 
114. 
116. 
116. 
120. 
125. 
130. 
137. 
144. 
143. 

// 

ISO 

140 
130 
120 

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130 

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1912               157.9 

154.2 

110 

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uo 

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100 

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90 

A 

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1     1     1     1     1     1     1 

no 

^5IMPLE    AVERAGE    OF    THE    RELATIVE    PF?ICES    OF 

2rELATIV£  prices  weighted  according    to  the   AVERAGE  CONSUMPTION 

IS  PRINCIP/VU   ARTICLES  OF  TOOD. 

OF     THE  VARIOUS   ARTICLES   OF    FOOD    IN  WORKINSMEN'3  FAMILIES. 

fr—  e.-.-..  ofd..  St.t^.t:<..,U.S.D.;,..t~.,t.( 

L.I.-                                                                                                                                                                                                      c.,„,,..  ..)!  v..  J.  .».. 

Courtesy  of  F.  J.  Warm,  Washington,  D.  C 

Fig.  95.  Relative  Retail  Prices  of  Fifteen  Principal  Articles  of  Food  in  the  United 
States,  1890  to  1912,  by  Simple  Averages  and  by  "Weighted  Averages.  Average 
Prices  for  the  Years  1890  to  1899,  Inclusive,  Were  Taken  as  100  Per  Cent 

The  solid  line  shows  ordinary  averages  of  the  prices  for  each  year  considered.  In  order  to  get  the  data  for 
the  dotted  line,  estimates  were  carefully  made  of  the  average  consumption  in  workingmen's.  families 
of  each  of  the  fifteen  various  articles  of  food.  The  food  prices  were  then  "weighted"  in  proportion  to 
the  quantities  of  each  kind  actually  consumed  and  the  averages  shown  by  the  dotted  line  were  obtained. 
The  prices  of  foods  to  the  workmen  did  not  increase  as  much  as  the  simple  averages  shown  by  the  solid 
line  would  indicate 

There  is  such  a  great  quantity  of  data  arranged  in  convenient  form 
for  reference,  it  seems  hkely  that  a  person  wishing  to  study  railroad 
operation  could  obtain  more  insight  into  present-day  railroad  condi- 
tions by  two-hours'  study  of  this  series  of  charts  than  he  could  pos- 


104 


GRAPHIC    METHODS 


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CURVE    PLOTTING  105 

sibly  obtain  by  two  months  of  reading  the  reports  of  transportation 
companies  and  the  pages  of  railway  journals,  and  of  asking  questions 
from  railroad  executives. 

A  heavy  line  in  Fig.  95  shows  the  relative  average  prices  of  fifteen 
articles  of  food  used  in  workmen's  families.  Since  the  fifteen  articles 
of  food  are  not  consumed  in  equal  quantities,  or  in  equal  value,  it  was 
necessary  to  take  into  account  the  actual  quantity  or  value  used  of 
each  kind  of  food.  This  was  done  by  the  method  usually  designated 
by  the  name  "weighted  averages".  It  is  obviously  of  less  importance 
to  the  workingman  if  the  price  of  salt  should  increase  500  per  cent 
than  if  the  price  of  bread  or  meat  should  increase  50  per  cent.  When 
the  fifteen  articles  of  food  are  considered  by  simple  averages,  all  foods 
are  considered  as  though  used  in  equal  quantities  and  a  very  great 
increase  in  the  value  of  some  one  food  would  seriously  affect  the  simple 
average  even  though  that  food  is  consumed  in  only  small  quantity. 
By  weighted  averages  the  actual  price  of  any  food  is  multiplied  by 
the  budget  percentage  figure  showing  the  percentage  of  that  food 
used.  The  products  resulting  from  the  multiplication  are  added  for 
each  year,  and  the  totals  or  averages  are  compared  on  a  percentage 
basis  to  give  a  corrected  comparison  by  weighted  averages  of  food 
prices  in  different  years.  The  weighted  averages  represent  more 
accurately  than  simple  averages  the  increases  in  food  prices  as  they 
really  affect  the  pocketbook  of  the  workingman.  It  will  be  seen  at 
the  right  of  Fig.  95  that  the  heavy  line  for  simple  averages  is  consider- 
ably higher  than  the  dotted  line  representing  the  weighted  averages. 
This  shows  the  amount  of  error  which  would  have  resulted  in  this 
particular  study  if  only  simple  averages  had  been  used  for  comparison 
instead  of  weighted  averages.  Weighted  averages  are  of  very  great 
importance  in  most  studies  relating  to  the  cost  of  living,  and  they 
could  be  used  in  other  work  much  more  widely  than  at  present  if  their 
importance  and  utility  w^ere  more  generally  understood.  It  is  un- 
fortunate.  that  in  Fig.  95  the  term  "relative  prices"  is  used  in  the 
lower  portion  of  the  chart  as  the  key  for  the  dotted  line.  The  simple 
averages  show  relative  prices  also  and  the  term  "relative  prices" 
means  practically  nothing.  The  dotted  line  could  more  properly  be 
referred  to  by  the  term  "weighted  averages"  as  used  in  the  title  at 
the  top  of  the  chart. 

Fig.  96  is  an  example  of  a  type  of  chart  which  can  be  of  great 
assistance  to  the  chief  executive  of  any  corporation  having  a  business 


106  GRAPHIC    METHODS 

seriously  affected  by  the  ups  and  downs  in  financial  conditions  af- 
fecting the  country  as  a  whole.  In  this  chart,  a  study  has  been  made 
of  supply  and  demand  in  the  hope  of  getting  some  basis  for  prediction 
in  regard  to  periods  of  financial  depression.  The  various  factors 
which  might  affect  prosperity  in  steel  construction  work  are  assembled 
here  on  one. chart  so  that  the  whole  situation  may  be  studied  con- 
veniently and  thoroughly.  In  a  chart  of  this  kind  some  estimates 
and  approximations  must  be  made  because  it  is  usually  impossible 
to  obtain  accurate  data  to  the  extent  desired.  For  work  of  this  nature 
it  will  ordinarily  be  found  that  a  little  "horse-sense",  used  in  making 
estimates  for  missing  data,  will  permit  the  construction  of  a  chart 
giving  an  astonishingly  large  number  of  suggestions  useful  in  deter- 
mining the  policy  of  a  business,  so  that  expansion  and  contraction 
may  be  in  harmony  with  the  basic  financial  conditions  of  the  country. 


Chapter  VII 
COMPARISON  OF  CURVES 

THERE  are  many  men  who  from  long  experience  have  become 
so  skillful  that  they  can  glance  down  a  column  of  figures  and 
obtain  quickly  a  good  idea  as  to  the  high  points  and  the  low 
points  shown  by  the  figures  taken  as  a  whole.  When  it  comes  to 
considering  two  or  three  columns  of  figures  simultaneously  to  see 
whether  there  is  a  similarity  in  the  fluctuations  shown  by  the  various 
sets  of  figures,  the  number  of  men  who  can  intelligently  grasp  the 
facts  presented  are  rather  few.  It  is  in  just  such  problems  as  these- 
where  a  number  of  different  sets  of  data  must  be  compared,  that  curves 
have  tremendous  advantage  over  presentation  by  columns  of  figures. 
A  man  must  be  almost  a  genius  to  grasp  quickly  the  facts  contained 
in  several  parallel  columns  of  figures,  yet  anyone  of  average  intelligence 
can  interpret  correctly  a  chart  which  has  been  properly  made  for  the 
presentation  of  curves.  Though  there  are  numerous  convenient  meth- 
ods which  are  useful  in  comparing  curves,  we  can  take  up  here  only 
the  few  of  those  which  are  likely  to  be  of  most  frequent  use  to  the 
average  reader. 

Fig.  97  brings  out  the  facts  of  its  subject  matter  with  splendid 
clearness.  There  are  relatively  few  men  who  could  interpret  quickly 
the  data  for  this  chart,  if  the  data  were  shown  to  them  only  as  two 
separate  columns  of  figures.  When  a  chart  like  that  shown  in  Fig.  97 
is  used,  no  mental  effort  is  required  to  get  at  the  gist  of  the  matter, 
and  the  facts  can  be  obtained  much  more  rapidly  than  would  ever 
be  possible  by  observing  columns  of  figures  alone. 

A  chart  like  that  used  in  Fig.  97  can  be  prepared  from  tabulated 
figures  by  any  ordinary  draftsman  in  less  than  one  hour  of  work. 
The  cost  of  making  a  line  cut  is  probably  no  more  than  the  cost 
of  setting  the  type  if  the  data  are  to  be  shown  by  tabulated  fig- 
ures.    The  space    required    for  a    chart   like    Fig.   97    is   very  little 

107 


108 


GRAPHIC    METHODS 


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more  than  would  be  required  for  the  tabulated  figures,  and  if  there 
is  any  serious  limitation  on  space,  Fig.  97  could  be  much  re- 
duced in  size  without  detracting  from  its  clearness. 

Health-department 
reports  are  not  usu- 
ally of  interest  to  the 
layman.  Yet  health- 
department  reports, 
well  presented,  may 
be  of  as  much  popular 
interest  as  a  well- 
written  magazine  ar- 
ticle. Fig.  98  is  taken 
from  a  commendable 
report  by  the  health 
department  of  the 
city  of  Boston.  In 
the  report  itself,  dif- 
ferent colors  of  ink 
were  used  for  the 
various  curves,  with 
the  effect  of  empha- 
sizing the  contrast. 
Though  the  colored  inks  assisted  in  catching  the  eye  of  the  reader, 
the  chart  with  curves  designated  by  letters  is  usually  sufficient  for 
all  practical  purposes  whenever  the  curves  do  not  cross  over  each 
other  in  such  manner  as  to  be  confusing.  As  mentioned  elsewhere, 
a  certain  slope  of  a  curve  plotted  on  rectangular  co-ordinate  paper 
does  not  in  itself  indicate  a  greater  or  less  amount  of  increase  or  de- 
crease than  holds  true  for  some  other  curve  having  a  different  slope. 
The  slope  of  a  curve  plotted  on  paper  with  ordinary  co-ordinate  ruling 
depends  largely  on  whether  the  data  of  the  curve  are  in  large  figures, 
so  as  to  bring  the  curve  near  the  top  of  the  chart,  or  in  small  figures, 
bringing  the  curve  near  the  bottom  of  the  chart.  In  Fig.  98  the  fact 
that  curve  A  slopes  more  than  curve  C  is  due  to  the  fact  that  curve  A 
is  placed  higher  on  the  vertical  sCale  of  the  chart  than  curve  C.  A 
little  study  will  show  that  the  reduction  in  mortality  portrayed  by 
curve  A  is  much  less  on  a  percentage  basis  than  that  depicted  by 
-surve  C,  yet  curve  A  has  the  steeper  slope.     The  slope  of  these  two 


No.  of 
Calls 
11.000 

10,000 


8,000 
7,000 


6.000 


4,000 
3P00 


2000 


1,000 


123-4    56789    10  II   12   t     23-456769    lO  11    12 
AJM.  P.M. 

Dala  of  the  New  York  Edison  Company 

Fig.  97.  Number  of  Telephone  Messages  Each  Hour 
for  One  Day  in  a  Business  District  in  New  York  City 
as  Compared  with  a  Residence  District 

Solid  line,  the  "Broad"  exchange — a  typical  business  exchange 
Dotted  line,  the  "Riverside"  exchange — a  typical  residence  exchange 
Note  the  great  number  of  business  calls  after  mail  has  been  opened  in 

the  morning  and  after  return  from  lunch.     In  the  residence  district 

there  is  much  morning  shopping  by  telephone 


COMPARISON    OF    CURVES 


109 


curves  can  best  be  compared  if  a  pencil  line  is  drawn  in  such  manner 
that  the  peaks  above  the  pencil  line  are  approximately  equal  to  the 
valleys  below  the  pencil  line  for  each  curve. 

Fig.  99  contains  some  interesting  information.  Though  the  chart 
proves  fairly  well  the  close  dependence  of  the  price  of  cast-iron  pipe 
upon  the  price  of  the  pig  iron  from  which  it  is  made,  the  chart  is  never- 
theless misleading  in  that  the  first  glance  would  indicate  a  much 
greater  fluctuation  in  the  price  of  pig  iron  than  actually  occurred. 


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From  the  into  Annual  Report  of  the  Health  Department,  City  oj  Boston 

Fig.  98.     Deaths  in  Boston  of  Children  under  Five  Years  of 
Age,  under  One  Year,  and  from  Five  of  the  Principal 
Infectious  Diseases,  Expressed  as  a  Percentage  of  the 
'  Total  Mortality 

Curve  A.     Deaths  of  children  under  five  years  of  age  as  a  percentage  of 

the  total  mortality 
Curve  B.     Deaths  of  children  under  one  year  as  a  percentage  of  the  total 

mortality 
Curve  C.     Deaths  from  Diphtheria,  Scarlet  Fever,  Measles,  Typhoid  Fever 

and  Smallpox  as  a  percentage  of  the  total  mortality 
Note  that  Curve  A  shows  a  much  steeper  slope  than  Curve  C,  yet  Curve  C 

drops  in  1910  to  less  than  half  the  figure  for  1871.     Curves  plotted  by 

rectangular  co-ordinates  should  not  be  compared  by  the  slope  of  the 

different  curve  lines 

The  reader  is  apt  to  overlook  the  fact  that  the  vertical  scale  of  the 
chart  does  not  extend  below  $11  per  ton.  He  is  quite  likely  to 
think  that  the  price  of  pig  iron  had  all  the  rapid  fluctuations  which 
would  be  indicated  by  the  changing  vertical  distances  between  the 
pig-iron  curve  and  the  bottom  line  of  the  chart  itself.  The  amount 
of  fluctuation  would  look  much  less  if  the  chart  extended  to  the  zero 
line  of  the  vertical  scale. 


110 


GRAPHIC    METHODS 


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There  is  probably  a  fallacy 
in  Fig.  100  because  of  the  rise 
in  the  general  standard  of  liv- 
ing between  1901  and  1906.  It 
is  not  fair  to  the  1901  Princeton 
men  to  expect  that  they  would 
earn  as  much  immediately  after 
graduation  as  men  who  gradu- 
ated in  a  period  of  time  several 
years  later.  In  addition  to  this 
there  is  probably  another  serious 
fallacy  which  affects  all  three 
curves  shown  on  the  chart.  The 
income  figures  from  which  the 
curves  are  plotted  may  not  all 
be  shown  on  the  same  basis. 
Men  working  on  a  salary  have  | 
as  net  cash  all  the  money  they 
receive.  Men  in  professions  such 
as  law%  medicine,  etc.,  where 
office  rent  and  other  expenses 
are  likelj''  to  be  very  heavy, 
may  report,  as  earnings,  the 
total  amount  of  money  received 
without  making  corrections  for 
the  expenses  of  conducting  their 
business.  In  other  words,  they 
may  very  possibly  in  this  case  re- 
port gross  income  instead  of  net 
income.  Such  procedure  might 
tend  to  make  the  curves  for 
average  income  considerably 
higher  than  they  would  other- 
wise be. 

Complex  charts  made  up  of 
groups  of  bars  as  seen  in  Fig. 
101  are  much  more  common 
than  they  should  be.  This  type 
of   chart   is   very    annoying    to 


COMPARISON    OF    CURVES 


111 


read  because  it  is  difRcult  for  the  eye  to  follow,  through  the  whole 
series,  the  bars  representing  any  one  set  of  facts  which  may  be  of 
special  interest.  The  bar  method  is  in  itself  a  simple  one,  but 
when  the  bars  are  combined  in  the  manner  shown  in  Fig.  101  the 
presentation  becomes  really  more  complex  than  if  the  data  were  shown 
in  the  form  of  curves. 

Fig.  102  certainly  brings  out  the  information  of  Fig.  101  in  much 
better  form  than  any  in  which  it  is  possible  to  show  it  by  any  com- 
bination of  bars  either  vertical  or  horizontal.  The  person  who  is 
just  beginning  to  chart  data  ^f^^^^^ 
which  he  has  used  formerly 
in  tabulated  form  is  often  ^ooo 
surprised  to  find  how  many 
inconsistencies  exist  in  the 
data  and  how  many  different 

•^  1000 

things  there  are  which  must 
be     allowed     for    by    some    500 
method  of  estimate.    In  Fig. 
102  the  data  for  the  United 

Kingdom    are    expressed    in  c^lsoe.     -Erotg'ol'. IISSS^B'^' 

net  tons,  and  for  the  United  pig.  100.  Comparison  of  the  Earnings  for  Five 
States  in  gross  tons.  Though.         Years  after  Graduation  of  the  Yale  University 

some  correction  of  the  forms  ^^SLEnTfic  School  ctss'otlp^e: 
of  the  curves  as  they  appear  and  the  Princeton  University  Class  of  1901 

in      this      chart      would     of  There  is  a  fallacy  in  making  this  comparison.     The  standard  of 

living  undoubtedly  went  up  between  1901  and  1906 

course  have  to  be  made  to 

get  a  true  comparison  of  the  shipping  of  the  two  countries,  for  our 
purpose  the  thing  of  greatest  interest  is  the  general  tendency  of  ship- 
ping in  the  two  countries.  This  we  can  study  fairly  well  from  the 
general  shape  of  the  different  curves,  even  though  the  curves  cannot 
strictly  be  compared  with  each  other  in  so  far  as  total  quantities  are 
concerned. 

Fig.  103  shows  a  convenient  method  for  determining  what  fluctua- 
tions in  the  different  months  of  the  year  are  typical  for  any  subject 
being  studied.  Instead  of  plotting  one  continuous  curve  by  months 
for  a  long  series  of  years  to  a  rather  small  horizontal  scale,  a  large 
horizontal  scale  is  used  and  a  separate  curve  is  drawn  for  each  year. 
The  curves  for  different  years  are  placed  one  above  the  other,  so  that 
any  fluctuations  which  appear  in  the  same  months  year  after  year 


112 


GRAPHIC    METHODS 


will  be  apparent  from  the  similarity  in  the  shape  of  the  curves  for 
the  different  years. 

In  order  to  use  a  fairly  large  vertical  scale  so  as  to  make  the  fluc- 
tuations stand  out  clearly,  it  was  necessary  to  avoid  entirely  the 
zero  lines  for  the  curves  plotted  in  Fig.  103.  The  omission  of  the  zero 
ffl^  Tonnage  engaged  m  Foreign  Trade  lines  may  cause  the  fluctuations 
dZ]  Tonnage  engaged  in  DomesticTrade        f^'Om    month    to    month    to    appear 

greater  than   their  true  size  would 

Amounts  in  thousands  of  tons 


I 


"I 


Gross  tonnage  given  for  United  States 
Net  tonnaqegivenfbr  United,  Kingdom 


I 

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warrant.     It  is  sometimes  possible 

to    plot    a    chart    on    the    general 

scheme  of  Fig.  103  so  as  to  use  zero 

lines,  but  many  times    it  will    be 

found  that   the  zero    lines  cannot 

be  used  without  adding  confusion. 

Though  it  would  be  preferable  to 

have    the    zero  lines  included,  the 

gain   due   to    the    arrangement    of 

the    curves     as     shown    here    for 

comparative     purposes     is     great 

enough  to  offset  the  disadvantage 

of  not  having  the  zero  lines  on  the 

chart. 

The  zinc  plate  for  Fig.  103  was 

prepared  directly  from  typewritten 

copy,  with  no  handwork  involved 

except  to    make    heavier    some  of 

the  green  background  lines  and  to 

draw  the  actual  curves  themselves. 
Fig.  loi.     Comparison  since  1850  of  the  ^t  i^*       •     t?-      mo  +1    4^  ai  4-1, 

Merchant  Tonnage   of  the   United  Notice  m  Fig.  103  that  the  month 

Kingdom  with  that  of  the  United  at  the  left  of  the  chart  is  December, 

States.    Gross  Tonnage  is  Given  for  ^^d  that  the  point  plotted  in  each 
the  United  States  and  Net  Tonnage  p      -rx  i  i      i   p     • 

for  the  United  Kingdom  case  tor  December  at  the  leit  is  ex- 

Tiie  chart  is  arranged  backwards  in  that  it  reads   actly  the  SaUlC  aS   the  point  plottcd 
from  right  to  left.     At  first  sight  one  thinks    »  ,•■  -j-.  U  1  +     +1 

e\erything  is  growing  smaller  instead  of  larger.  lOT  ZllQ  J^ecemoer  SllOWU  at  tUe 
The  different  bars  so  closely  grouped  together  ^l^y.^  ^f  fl-.p.  nrp^Pf^rlino-  n^^v\T(^  "Rv 
are     exceedingly     difficult     to     interpret.     See   Tl^UL    OI    tllC    preceomg     CUrVC.       Dy 

F^g- 102  repeating  the  last  month  of  each 

curve  in  this  manner,  the  interpretation  of  the  curves  is  much  sim- 
plified so  that  the  reader  can  see  at  once  what  has  been  the  tendency 
of  the  curve  from  December  to  January  each  year.    If  the  December 


CJ  o  c? 

r-         u?         LO 

22         22         22 

Philadelphia  Commercial  Museum 


COMPARISON    OF    CURVES 


113 


point  were  not  represented  at  the  left,  it  would  be  necessary  for  the 
reader  to  glance  several  times  from  the  left-hand  end  of  one  curve 
to  the  right-hand  end  of  the  preceding  curve  to  determine  in  his  own 
mind  just  what  changes  had  occurred  from  December  to  January 


Millions 

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Fig.  102.  Comparison  since  1850  of  the  Merchant  Ton- 
nage of  the  United  Kingdom  with  that  of  the  United 
States 

Gross  tonnage  is  given  for  the  United  States  and  net  tonnage  for  the 
United  Kingdom.  Solid  lines  United  States,  dotted  lines  United 
Kingdom.  The  "total"  figures  are  not  strictly  comparable  because 
of  the  difference  in  registration  method.  The  general  tendencies 
of  the  curves  are  instructive,  however.  Note  the  reduction  in  the 
foreign  trade  of  United  States  since  the  Civil  War  and  the  steadily 
increasing  foreign  trade  of  the  United  Kingdom 

at  the  end  of  each  year.  The  repetition  of  the  point  for  the  last  month 
in  each  year  saves  time  to  the  reader  and  also  insures  against  errors 
which  might  otherwise  occur  in  the  interpretation  of  the  chart. 

In  Fig.    104   three   distinct  subjects   are  compared  on  one  chart 
and,  at  the  same  time,  the  data  for  each  subject  are  shown  for  three 


114 


GRAPHIC    METHODS 


WSTSLY   AVERAGES  OP  BUTTER  PAT  HT  HfDIAHAPOLIS  MILK. 

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0.    ^ 

Data  of  J.  J.  Hinman,  Jr.,  Indianapolis  Department  of  Public  Health 

Fig.  103.  Monthly  Averages  of  Butterfat  Contained  in  Milk  on  the  Indianapolis 
Market,  1906  to  1913.  The  Curves  Represent  Averages  from  Several  Hundred 
Samples  each  Month 

In  order  to  find  what  fluctuations  are  typical  for  various  months  of  the  year,  it  is  convenient  to  chart  the 
data  as  seen  here  with  curves  for  different  years  one  above  the  other.  Definite  peaks  in  April  and  in 
October  or  November  are  seen  at  once.  This  chart  is  drawn  on  the  same  universal  co-ordinate  paper 
shown  also  in  Fig.  57,  Fig.  130,  Fig.  134  and  Fig.  156 


COMPARISON    OF    CURVES 


115 


IAN        FFR        MAR       APR        MAY       JUNE      JULY       AUG      SEPT      OCT        NOV        DEC. 

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Comparative  Monthly  Earnings  and  Expenses  Per  Mile  ct  Road 

Frank,  Haigh  Dixon,  in  the  Railway  Age  Gazette 

Fig.  104.  Comparative  Monthly  Earnings  and  Expenses  per  Mile  of  Road  of  Steam 
Railroads  in  the  United  States  Having  Annual  Operating  Revenues  of  $1,000,000 
or  More 

It  is  frequently  convenient  to  superimpose  curves  for  successive  years,  so  that  seasonal  similarities  and  definite 
increases  or  decreases  may  be  accurately  studied.  Compare  this  chart  with  Fig.  103  and  also  with  Fig. 
204.  It  would  be  better  if  the  heavy  line  border  around  the  edge  of  this  chart  were  omitted.  The 
heavy  line  at  the  bottom  does  not  coincide  with  the  zero  line  and  the  reader  may  be  misled  by  reading 
the  chart  from  the  border  line 


different  years  so  that  comparisons  between  these  different  j^ears  are 
easily  made.  This  scheme  of  superimposing  curves  for  different  years 
is  a  very  common  one  that  frequently  gives  an  arrangement  more 
convenient   than   could   otherwise   be   obtained.     It   will   be   noticed 


116 


GRAPHIC    METHODS 


1900 
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— 

Comparison  of  Electrical  Output  and  Coal  Consumption  for  Dec.  1912 
and  Dec.  1911,  in  Plant  of  Acker,  Merrall  &  Condit  Co.   Building. 

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Dec.1911     3     4     5     6     7     8     9    10  11    12   13   14   15    16  17   18  19    20  21  22  23    24   25  26   27  28   29  30   31    1 
Dec.1912      1     2     3     4     5     6     7     8     9     10   11   12    13    14   15    16  17    18  19    20  21   22  23   24  25  26   27  23  29  30 
S  S  S  C  S 


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The -Engineering  it agazine 

Fig.  105.    Comparison  of  Daily  Electrical  Output  and  Daily  Coal  Consumption  of  a 
Power  Plant  for  the  Same  Month  in  Two  Succeeding  Years 

There  is  a  relatively  small  quantity  of  power  needed  on  Sundays.  In  order  to  make  possible  a  comparison 
of  the  two  curves  for  different  years  the  horizontal  scales  for  days  were  so  placed  that  the  Sundays  would 
coincide.  With  curves  thus  arranged,  the  low  points  caused  by  Christmas  do  not  fall  on  the  same  vertical 
line,  since  Christmas  is  fixed  by  the  day  of  the  month  instead  of  by  the  day  of  the  week 


COMPARISON    OF    CURVES 


11, 


in  this  chart  that  the  December  points  have  not  been  repeated  at  the 
left  and  the  reader  is  forced  to  glance  between  left  and  right  in  order 
to  make  certain  in  his  'own  mind  just  what  changes  occurred  from 
December  to  January  each  year.  It  can  be  seen  that  the  January 
figures  for  "Operating  Revenues"  are  all  considerably  lower  than 
the  December  figures,  but  even  so  the  reader  has  no  clear  idea  of 
the  slope  of  the  lines  which  would  be  most  typical  to  portray  the 
changes  from  De- 
cember to  January 
in  each  year.  This 
question  of  repeat- 
ing one  point  for 
curves  of  different 
years  superimposed 
is  referred  to  also  in 
Chapter  XIII,  Fig. 
204. 

Fig.  105,  Fig.  106, 
and  Fig.  107  are  self- 
explanatory.  They 
show  some  interest- 
ing applications  of 
curves  to  special 
problems,  and  dem- 
onstrate the  great 
convenience  which 
might  result  if  curves 


Edwin  D.  Dreyfus,  in  Industrial  Engineering 

Fig.  io6.  Average  Temperature  at  Pittsburgh,  Pa.,  for 
Each  Hour  in  the  Day  for  Different  Months  in  the 
Year.  Plotted  for  Monthly  Averages  of  Twenty- 
Years  Observations  (1891-1910)  of  the  United 
States  Weather  Bureau 

It  would  be  impossible,  using  only  columns  of  figures,  to  put  this  informa- 
tion in  such  convenient  form  for  reference  and  comparison.  The 
broad  horizontal  line  at  10  degrees  on  the  vertical  scale  of  this  chart 
and  of  Fig.  107  is  unfortunate  since  that  line  has  no  special  significance 
for  persons  reading  the  chart 


could  be  more  generally  used  for  presenting  every-day  facts  to  non- 
technical readers. 

In  Fig.  108  we  see  the  application  of  curves  to  the  kind  of  data 
of  which  it  would  be  extremely  difficult  to  give  a  clear  understanding 
if  only  columns  of  figures  were  available  in  the  presentation.  With 
these  two  curves  we  are  not  so  much  interested  in  the  total  height 
of  the  peak  as  in  the  general  shape  of  the  curve  on  either  side  of  the 
peak,  showing  whether  there  are  any  laws  of  uniformity  in  the  increase 
of  the  flood  level  and  in  the  speed  with  which  the  flood  subsided.  The 
two  curves  in  Fig.  108  are  quite  different  in  their  shape,  although  they 
were  taken  for  the  same  period  of  time  in  districts  not  widely  sepa- 
rated.    The  size  and  general  character  of  different  water-sheds  have 


118 


GRAPHIC    METHODS 


a  great  effect  on  the  nature  of  the  floods  which  may  result  from  any 
definite  rainfall. 

In  Fig.  109  also  we  are  particularly  interested  in  comparing  the 
shape  of  the  curves  for  the  distinctly  different  materials  under  con- 
sideration. Here  the  curves  represent  reactions  affected  by  the  defi- 
nite laws  of  physics,  and  we  can  join  the  plotted  points  resulting  from 
different  observations  so  as  to  get  smooth  curves.  Work  in  engineer- 
ing, physics,  and  chemistry  depends  very  largely  on  the  interpre- 
tation of  smooth  curves  like  these,  and  world  progress  would  be 
greatly  retarded  if  the  graphic  method  were  not  available  to  assist 
in  preserving  and  interpreting  the  results  of  elaborate  experiment  and 

voluminous  research. 
In  selecting  a 
scale  for  Fig.  110  the 
draftsman  is  torn  be- 
tween a  desire  to 
show  the  San  Fran- 
cisco fire  peak  at  its 


correct  height,  and 
an  opposing  desire  to 
show  on  a  large  scale 
the  data  for  a  whole 
series  of  years  so 
that  the  fluctuations 
from  month  to 
month  maybe  clearly 
defined.  It  seemed 
best  to  cut  off  the 
top  of  the  San  Fran- 
cisco peak  so  as  to 
show  the  monthly 
data  on  a  scale  large 
enough  to  assure 
clearness.  To  get  the  correct  slope  for  the  two  sides  of  the  San  Fran- 
cisco peak,  a  piece  of  paper  was  laid  down  adjoining  the  chart  and  a  point 
was  located  in  the  correct  position  for  the  top  of  the  San  Francisco 
peak.  The  sides  of  the  peak  were  then  drawn  so  that  they  would 
meet  at  that  point  if  extended.  Even  though  the  figures  for  the  San 
Francisco  peak  are  given  at  the  top  of  the  chart  where  the  peak  is 


Ediein  D.  Dreyfus,  in  Industrial  Engineering 

Fig.  1 07.  Mean  Temperatures  for  Each  Month  in  the  Year 
at  Different  Cities.  Plotted  from  Records  of  the 
United  States  Signal  Service  and  of  Blodgett's 
Climatology  of  the  United  States 

Information  for  eight  different  cities  is  so  given  that  comparisons  are 
easily  made.  Note  the  different  lines  used  here  instead  of  colors. 
Since  Pittsburgh  was  the  city  under  prime  consideration,  the  Pitts- 
burgh line  was  made  heavy  that  it  might  be  most  clearly  seen.  This 
chart  gives  a  great  amount  of  data  in  smaller  space  than  would  be 
required  to  show  the  facts  by  any  method  othe"  than  the  use  of  curves 


1 


COMPARISON    OF    CURVES 


119 


broken  off,  most  readers  will  not  imagine  correctly  the  great  height 
to  which  that  peak  would  extend  if  it  were  shown  in  full.  The  chart 
could  have  been  greatly  improved  if  the  upper  portion  of  the  peak 
had  been  drawn  in  full  size  horizontally  as  though  hinged  near  the 
upper  margin  of  the  drawing.     Since  the  full  height  of  the  peak  is 


soooo 


O  25000 


25       26       27       28       29 
March.  |9I3 


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2000 

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27      28      29 

March.  1913 


Engineering  Record 


Fig.  io8.     Comparison  of  Flood  Rise  in  Two  Rivers  in  New  York  State  During  the 

Floods  of  March,  1913 

In  the  preceding  illustrations  of  this  chapter  there  has  been  such  similarity  in  the  shape  of  the  curves  con- 
sidered that  they  were  superimposed  for  comparison.  Here  the  curves  are  of  different  shape  and  they  are 
shown  in  separate  fields  so  that  the  contrast  may  be  more  striking.  The  chart  at  the  left  should  have 
had  the  zero  line  shown.  It  is  dangerous  to  base  conclusions  on  the  comparison  of  two  curves  unless 
the  zero  lines  are  shown  in  each  case 


NICKEL 

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Iron  Age 

Fig.  109.  Comparison  of  Different  Kinds  of  Steel  Containing  0.2  per  cent  Carbon,  as 
shown  by  Tensile  Tests  on  Specimens  100  mm.  long  and  13.8  mm.  diameter.  The 
Vertical  Scale  Represents  Thousands  of  Pounds  per  Square  Inch  and  also  Per- 
centage of  Contraction  or  Elongation 

The  heavy  line  shows  ultimate  strength 

The  dash  line  shows  elastic  limit 

The  dash-dot  line  shows  percentage  contraction 

The  light  line  shows  percentage  elongation 

In  this  chart  the  thing  of  greatest  interest  is  the  contrast  seen  by  comparing  the  shapes  of  the  curves  foi 
different  steels.  Though  it  is  best  to  have  curves  of  such  distinct  shape  plotted  in  separate  fields,  ii 
is  ordinarily  most  convenient  to  have  the  fields  themselves  placed  vertically  instead  of  horizontal!" 


420 


GRAPHIC    METHODS 


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COMPARISON    OF    CURVES 


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almost  three  times  the  height  of  the  portion  shown  on  this  illustration, 
it  would  be  necessary  to  make  two  other  hinges  in  the  horizontal 
extension  so  that  the  peak  could  be  bent  downward  and  turned  back- 
ward from  right  to  left,  giving  something  of  a  spiral  effect.  Though 
this  bent  peak  may  seem  rather  artificial,  it  is  quite  certain  that  the 


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1911 


1901         1302        1903        1904        1905        1906        1907        1908       l909 

L_J  New  Building  BB  Fire  Losses 

Note-  values  are  given  in  Millions  of  Dollars 

Adapted  from  Article  by  Roger  W.  Babson  in  the  New  York  Times 

Fig.  III.    Yearly  Value  of  New  Building  Construction  and  Yearly  Value  of  Buildings 
Destroyed  by  Fire  in  the  United  States,  igoi  to  iQii,  Inclusive 

With  this  arrangement,  the  percentage  value  destroyed  by  fire  can  be  seen  more  readily  than  from  the 
arrangement  used  in  Fig.  110.  The  fluctuation  from  month  to  month  cannot,  however,  be  seen  here. 
If  both  charts  are  used,  they  supplement  each  other  very  well.  Remember  that  for  these  two  charts 
the  buildings  destroyed  are  not  necessarily  the  new  buildings  whose  value  is  given.  The  black  area 
represents  only  the  value  of  buildings  destroyed  whether  new  or  old.  Note  the  Ben  Day  shading 
on  the  upper  ends  of  the  bars  and  the  figures  for  the  data  from  which  the  chart  was  made 


GRAPHIC   METHODS 


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Fig. 


tapering  form  of  the  horizontal  extension  of  the  peak  would  be  under- 
stood by  even  the  untrained  reader,  much  more  certainly  than  the 
chart  as  shown  here  with  only  the  figures  to  indicate  the  full  extent  of  the 
loss  which  occurred  in  the  San  Francisco  fire. 

While  Fig.  110 
gives  some  general 
idea  of  the  propor- 
tion which  American 
fire  losses  bear  to 
the  value  of  new 
building  construc- 
tion, the  two  fluctu- 
ating curves  make  it 
difficult  for  the  reader 
to  make  an  estimate 
of  the  percentage 
losses  year  by  year. 
Fig.  Ill  supplements 
Fig.  110,  and  gives 
for  each  year  the 
total  values  for  new 
building  construction 
and  the  total  values 
of  buildings  de- 
stra;y'ed  by  fire.  Here 
the  percentages  of 
the  fire  loss  are  quite  obvious  when  judged  by  the  extent  to 
which  the  black  ink  covers  the  shaded  bar  representing  new  build- 
ing construction.  Figures  are  given  in  each  case  for  the  reader 
who  may  care  to  work  out  the  actual  percentage  ratios.  It  must 
not  be  assumed  from  the  titles  of  Fig.  110  and  Fig.  Ill  that  the 
buildings  destroyed  by  fire  are  the  same  buildings  whose  value  is  re- 
corded in  the  charts  as  "new  building  construction."  The  rapid 
advance  in  the  use  of  fireproof  materials  makes  it  likely  that  the  fire 
losses  were  more  largely  from  older  buildings,  built  by  methods  which 
gave  a  structure  less  fireproof  than  the  average  for  buildings  put  up 
in  recent  years 

Fig.  114  shows  an  error  in  curve  plotting  into  which  it  is  very 
easy  for  an  inexperienced  person  to  slip.   One  vertical  scale  is  relatively 


1 


5.00  5.30  6.00  6.30  7.00  7.30  8.00  8.30  8.0O 

P  M  Time  Monday.JIarch  14,  1910  P.  M. 

Sam.  L.  Nav^lalv.  in  Jovmal  American  Society  of  Mechanical  Engineers 

112.  Record  of  Test  of  a  Steam  Turbine  of  10,000 
Kw.  Normal  Rating  at  Plant  of  City  Electric  Com- 
pany, San  Francisco,  California 

The  different  curves  shown  in  this  chart  supplenaent  each  other  so  as 
to  give  all  the  data  on  one  chart  in  compact  form.  The  scale  for 
each  curve  given  at  the  left  is  only  sufficient  to  show  the  maximum 
and  minimum  value  for  each  curve.  The  zero  lines  have  been 
omitted  entirely.  Though  charts  of  this  type  with  numerous  curves 
are  sometimes  desirable,  they  must  be  carefully  made  or  the  reader 
will  be  misled  by  the  fluctuations  of  some  one  curve  appearing  more 
prominently  than  the  data  would  justify 


COMPARISON    OF   CURVES 


123 


larger  than  the  other,  and  on  that  account  the  curves  have  been 
made  to  coincide  more  closely  than  they  would  have  done  if  both 
scales  had  the  same  zero  line.  In  making  comparisons  of  this  kind 
care  must  be  used  to  have  the  two  scales  start  from  the  same  zero 
line,  or  the  person  presenting  the  charts  will  be  open  to  the  unpleasant 
suspicion  of  attempting  to  "fake." 

If  the  reader  cares  to  see  how  these  two  curves  would  contrast  if 
properly  plotted,  the  left-hand  scale  for  "corn  yield"  can  be  changed 
so  that  the  different  horizontal  lines  will  be  represented  by  the  figures 
0,  7,  14,  21,  28,  etc.  The  data  for  "corn  yield"  can  then  be  plotted 
to  the  new  scale,  and  it  will  be  found  that  the  new  curve  does  not 
coincide  with  the  "rainfall"  curve  as  closely  as  does  the  "corn- 
yield"  curve  shown  in  Fig.  114.  Though  there  is  some  similarity  in 
the  shape  of  curves  correctly  plotted  from  these  data,  the  similarity 
is  not  nearly  so  exact  as  Fig.  114  would  indicate. 


1910-1911 

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TTTTnr^mtimiTt:?a4::"ntrtrmTT{'!'iiiiiii[i;iiitnrtiTTntT7tTiTTi]iiiiiiiiiini^ 


Courtesy  of  System 

Fig.  113.    Records  of  Freight-Train  Operation  on  a  Large  Eastern  Railroad 

Here,  as  in  Fig.  Wl,  the  lero  lines  are  not  given  and  the  reader  must  watch  the  left-hand  scales  carefully 
to  study  percentage  fluctuation.  Comparison  between  curves  cannot  be  made  accurately  by  judging 
from  the  slope  or  from  the  total  fluctuation  of  the  curves  on  the  page.  Percentage  increases  or  decreases 
for  one  curve  compared  with  percentage  increases  or  decreases  of  other  curves  give  the  best  basis  for 
comparison 

Curves  well  made  ordinarily  need  no  embellishment.  Anything  used  for  an  eyecatcher  should  apply  definite- 
ly to  the  subject  matter  of  the  curves.  Here  the  subject  is  freight-train  operation,  but  the  picture  shows 
the  interior  of  a  passenger  train 


J24 


GRAPHIC    METHODS 


Fig.  115  gives  a  good  example  of  a  total  curve  made  by  adding  the 
figures  for  different  curves.  Instead  of  using  addition  to  get  a  set 
of  figures  from  which  a  total  curve  may  be  plotted,  it  is  easier  in  most 
cases  to  get  the  location  of  the  total  curve  by  the  graphic  method. 
All  that  is  necessary  is  to  lay  off,  with  draftsman's  dividers,  successively 
on  each  vertical  line,  the  height  above  zero  at  which  each  of  the  dif- 
ferent curves  intersects  that  vertical  line.  The  totaling  curve  is 
drawn  through  the  points  thus  found.  When  there  are  not  too  many 
curves,  this  method  answers  admirably.  It  sometimes  happens  that 
actual  observations  for  the  data  of  different  curves  are  not  simul- 
taneously taken  and,  for  this  reason,  it  may  be  impossible  to  add  | 
the  actual  numerical  data  so  as  to  plot  a  total  curve.    In  such  cases, 

the  graphic  method 
of  stepping  off  the 
height  for  the  total 
curve  is  practically 
the  only  one  avail- 
able. After  each  of 
the  separate  curves 
has  been  plotted 
from  such  data  as 
may  exist,  it  is  a  very 
simple  matter  by  the 
graphic  method  to 
locate  the  total  curve 
from  the  separate 
curves.  A  sufficient 
number  of  vertical 
lines  are  used  to 
bring  the  points  on 
the  total  curve  close 
enough  together  to 
represent  fairly  the 
data  of  the  separate 
curves  which  are 
totaled. 


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'88     '89     ^0     '91      "92     "93      l94     "95     "96     '97     '98     "99     'GO     '01       02 

Adapted  from  PenTisylvania  Farmer 

Fig.  114.  Chart  to  Show  the  Dependence  of  Com  Yield 
upon  the  Quantity  of  Rainfall  during  the  Month  of 
July.    The  Yield  of  Com  is  Given  in  Bushels  per  Acre 

This  chart  is  misleading.  The  close  similarity  of  the  two  curves  has 
been  obtained  by  plotting  one  curve  on  a  larger  scale  than  that  used 
for  the  other  curve.  The  rainfall  curve  has  been  plotted  with  the 
bottom  of  the  chart  as  zero.  The  corn-yield  curve  is,  however,  drawn 
with  the  scale  starting  at  twelve. 


In  plotting  curves  relating  to  prices,  it  frequently  happens  that 
there  is  a  necessity  for  showing  in  the  chart  both  the  upper  and  lower 
limits  to  which  the  prices  may  fluctuate  in  any  given  period  of  time. 


COMPARISON    OF    CURVES 


125 


1 

900 
800 

Is 

tJ  c  700 

S  := 

o  a 

^600 

500 

Max. 
Load 

%  Max. 
1-2  Max. 
Lj  Max. 

1 

/ 

V 

/- 

X 

A -Hotel 

B  -  Apartment  House 

C- Department  Store 

D- Combined  Load  Curve 

E-  Loft  Building 

F-  Office  Building 

Note:  Combined  Load  Curve 
shown  in  true  size 

/ 

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7               9              11              1               3               5               7               9              11               1        ,,    3               5              7 
A.M.                                                                 P.M.                                                         A.M. 

XM  Mngine.(jiina  Masaaim 

Fig.  115.    Typical  Curves  Showing  the  Twenty-Four  Hour  Demand  for  Electricity 
during  the  Summer  Months  in  Various  Types  of  Buildings  in  New  York  City 

Curve  D  shows  the  fluctuations  in  the  load  on  a  power  house  supplying  all  of  the  buildings  represented  by 
curves  A,  B,  C,  E  and  F.  By  combining  loads  of  different  types,  the  power  plant  can  be  kept  more  con- 
tinuously busy  than  otherwise  possible.  After  the  other  curves  are  all  plotted,  curve  D  can  easily  be 
located  by  stepping  off  with  draftsmen's  di\-iders  on  each  vertical  line  the  heights  of  all  the  different 
curves  at  that  particular  line 

This  is  especially  true  where  curves  are  plotted  showing  the  fluctuations 
in  the  market  prices  of  stocks  or  bonds.  In  such  cases,  it  is  desirable 
to  plot  two  curves,  one  showing  the  minimum  prices  and  the  other 
showing  the  maximum  prices.  When  the  two  curves  lie  quite  closely 
together,  it  frequently  assists  in  the  clearness  of  the  chart  if  the  co- 
ordinate lines  are  erased  between  the  two  adjacent  curves.  The  erasing 
of  the  co-ordinate  lines  makes  the  curves  stand  out  much  more  dis- 
tinctly than  they  otherwise  would. 

Charts  on  the  general  type  of  Fig.  116  are  valuable  to  give  a  vivid 
comparison.  A  chart  of  this  kind  would  be  especially  striking  if  used 
in  advertising,  or  in  a  report  where  concentration  upon  only  one  gen- 
eral idea  was  needed,  without  a  great  amount  of  specific  detail.  Though 
Fig.  116  shows  that  telephone  rates  have  had  a  constantly  downward 


126 


GRAPHIC    METHODS 


trend  as  the  number  of  telephones  in  use  has  increased,  there  is, 
after  all,  no  real  proof  in  the  chart  that  the  rates  have  decreased 
in  proportion  to  the  increase  in  the  number  of  telephones  in  use. 
Fig.    116   stimulates   interest   and   makes   one  wish   to   plot   another 

chart  in  which  the 
number  of  telephones 
in  use  would  be  the 
horizontal  scale  and  ^ 
the  average  rate  paid 
would  be  the  vertical 
scale,  somewhat  on 
the  general  scheme 
of    Fig.    119.     The 


1898       1899        1900       I90i 


1906        1907        1908 

Courtesy  of  Data,  Chicago 


Fig.  ii6.    Chicago  Telephone  Rates  per  Year  Compared 
with  the  Number  of  Telephones  in  Use  in  Chicago 

It  is  the  object  in  this  chart  to  show  that  the  rates  have  been  consistently 
reduced  as  the  number  of  telephones  has  increased.  The  curves 
shown  earlier  in  this  chapter  have  varied  directly,  usually  going  up 
or  down  simultaneously.  Here  we  have  an  inverse  relation,  witli  one 
curve  coming  down  as  the  other  goes  up 


plotted  points  for 
different  years  on  a 
chart  of  the  kind 
suggested  would 
show  by  the  arrange- 
ment of  the  points  whether  the  prices  had  changed  exactly  in  accord- 
ance with  the  number  of  telephones  in  use. 

Fig.  117  has  been  very  carelessly  drawn  in  that  the  two  curves 
do  not  have  their  vertical  scales  start  at  the  same  zero  line.  The 
zeros  for  each  of  these  scales  are  so  close  to  the  curves  as  drawn  that 
it  would  have  been  a  very  simple  matter  to  have  made  one  zero  line 
for  both  scales  at  the  bottom  line  of  the  chart  itself.  The  adverse 
criticisms  of  Fig.  114  may  be  applied  to  this  chart  also. 

Though  the  two  curves  in  Fig.  117  seem  to  show  some  inverse 
relation,  since  one  curve  frequently  goes  up  when  the  other  curve  comes 
down,  the  chart  does  not  permit  any  measurement  by  which  the  degree 
of  correlation  can  be  determined.  The  student  who  wishes  to  experi- 
ment with  this  interesting  set  of  data  would  do  well  to  make  an  en- 
tirely new  chart  with  the  two  curves  plotted  from  one  zero  line.  After 
this  first  chart  has  been  made,  a  second  chart  can  be  drawn  in  which 
the  "Price"  curve  would  be  plotted  exactly  as  in  the  first  chart.  The 
curve  for  the  number  of  barrels  of  "Exports"  should,  however,  be  plot- 
ted downward  from  the  top  of  the  chart,  after  a  good  position  has  been 
selected  for  the  top  of  the  chart  so  that  the  "Exports"  curve  plotted 
downward  from  the  top  would  coincide  as  nearly  as  possible  with  the 
"Price"  curve  plotted  upward  from  the  bottom.    The  scales  for  the 


COMPARISON    OF    CURVES 


U7 


curves  in  the  second  chart  should  be  the  same  as  those  for  the  first 
chart,  so  that  there  may  be  no  "faking"  in  any  similarity  which 
may  show  up  in  the  shapes  of  the  two  curves.  It  frequently  happens 
that  the  relations  between  two  curves  are  such  that  the  most  striking 
presentation  can  be  obtained  by  plotting  one  curve  upside  down  so 
as  to  bring  the  two  curves  as  closely  into  coincidence  as  possible, 
and  the  scheme  should  be  kept  in  mind  as  it  is  frequently  of  assistance 
in  making  facts  stand  out  vividly. 


Courtesy  of  Pennsylmnia  Farmer 


Fig.  117.    Exports  of  Apples  from  the  United  States  as  Compared  with  the  Average 
Wholesale  Price  in  the  United  States 

A  little  inspection  shows  that  the  export  curve  usually  goes  up  when  the  price  curve  comes  down.  Though 
this  fact  indicates  an  inverse  relation  between  the  two  curves  under  consideration  it  does  not  give 
satisfactory  proof  that  exports  fluctuate  relatively  as  much  as  price. 

This  chart  is  likely  to  mislead  the  reader  because  the  two  vertical  scales  do  not  have  the  same  zero  line. 
Curves  compared  in  this  manner  without  having  a  common  zero  line  should  always  be  distrusted 

Another  interesting  study  can  be  made  from  Fig.  117  by  drawing 
a  chart  with  "Price"  as  the  horizontal  scale  and  quantity  of  "Exports" 
as  the  vertical  scale.  Dots  for  the  different  years  placed  on  such  a 
chart,  after  the  general  manner  of  Fig.  119,  will  appear  so  widely 
scattered  over  the  whole  field  that  the  reader  will  find  it  almost  hope- 
less to  draw  any  general  conclusion  from  the  arrangement  of  the 
dots.     Though  the  dots  indicate  by  their  position  a  general  tendency 


128 


GRAPHIC    METHODS 


for  exports  to  decrease  as  prices  increase,  there  would  seem  to  be 
so  many  complex  factors  entering  into  the  relation  that  no  very  gen- 
eral law  of  dependence  can  be  proved. 

It  can  be  seen  from  inspection  that  the  relations  existing  between 
the  two  curves  of  Fig.  118  are  much  closer  than  exist  between  the 
two  curves  of  Fig,  117.  It  is  unfortunate  that  in  Fig.  118,  as  well 
as  in  Fig.  117,  the  chart  was  carelessly  prepared  so  that  the  two  curves 
do  not  have  the  same  zero  line. 


Courtesy  of  Pennsylvania  Farmer 

Fig.  1 1 8.    The  Average  Price  of  Apples  in  the  United  States  as  Compared  with  the 

Total  Supply 

Here  again  an  inverse  relation  is  indicated,  but  the  chart  has  carelessly  been  made  with  the  two  vertical 
scales  starting  from  separate  zero  lines  so  as  to  cause  distrust  by  the  reader.  The  chart  is  printed  show- 
ing a  finely  ruled  co-ordinate  background,  though  only  every  tenth  line  is  desirable  for  the  reader.  The 
use  of  more  lines  than  necessary  should  be  avoided  as  it  tends  to  cause  confusion.  See  Fig.  119  as 
another  method  of  charting  the  same  data 

In  order  to  determine  just  how  closely  the  price  of  apples  depends 
upon  the  supply.  Fig.  119  was  prepared  from  the  data  of  Fig.  118. 
Though  the  dots  in  Fig.  119  represent  a  rather  long  series  of  years, 
they  nevertheless  have  a  fairly  symmetrical  arrangement  and  the 
general  tendency  might  be  approximated  by  a  smooth  curve  drawn 
as  shown.  It  must  be  remembered  that  there  are  many  conditions 
which  may  affect  the  position  of  these  dots  on  the  chart.    For  one  thing. 


COMPARISON    OF    CURVES 


129 


Price  per  Bbl 


1910 

\ 

19 

j\™l 

907 

«S 

s. 

906 

T« 

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.,^ 

199 

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^^ 

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<« 

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896 

the  standard  of  living  has  very  greatly  changed  in  the  period  of  time 
from  1895  to  1912.  Prices  in  recent  years  might  be  expected  to  be 
considerably  higher  than  in  the  earlier  years,  without  any  regard  to 
the  size  of  the  apple  crop.  Besides  this,  numerous  diseases  have 
affected  apple  trees  in  recent  years,  requiring  more  care  than  formerly 
to  produce  good  fruit.  This  would  also  have  some  tendency  to  raise 
prices  in  spite  of  the  tremendous  number  of  apple  trees  which  have 

come  into  bearing  in  the 
later  portion  of  the  period 
of  time  under  consideration. 
The  general  method  of  plot- 
ting shown  in  Fig.  119  is 
of  great  importance  and  it 
should  be  kept  in  mind 
whenever  two  curves  are 
found  having  similarities 
such  as  are  seen  in  Fig. 
118.  Other  examples  of  this 
method  of  plotting  to  study 

EO   E5   30   35   40   45   50   55   €0   65   70   75  ■•^  "  «/ 

Quantity  in  Millions  of  Bbis  ^jjg  corrcktiou  of  two  rcktcd 

Fig.  no.    The  Average  Price  of  Apples  in  the  i  •     .        -n  i.     f        j  •     4.1, 

United   States   as   Compared  with  the  Total  subjects  will  be  found  m  the 
Supply 

By  this  method,  the  positions  of  the  dots  on  the  chart  show 
whether  there  is  any  close  relation  between  supply  and 
price.     The  dots  fall  in  fairly  regular  order,  proving  better   information    for    tllC   Studcut 
than  Fig.  118  that  the  price  does  largely  depend  upon  the       „    r,'    j.  \ii^  l 

supply.  A  smooth  curve  has  been  drawn  to  represent  Ot  illStory .  V\  C  are  JlCre  lU- 
approximately  the  general  relation  between  supply  and  4.^„^„4.^J  r^artiVnlarK^  in  tli^ 
price  which  the  dots  might  seem  to  indicate.  Note  that  LCie&LCU  pdlLlcuidll^  ill  uie 
the  year  is  stated  for  each  dot  shown  rCCOrd  of  the   United  StatCS. 

That  curve  line  has  accordingly  been  made  much  heavier  than  any 
of  the  others,  so  that  it  may  be  brought  prominently  to  the  eye  of 
the  reader.  By  visually  projecting  the  curves  for  Russia  and  the 
United  States  beyond  the  limits  of  the  chart,  it  appears  that  we  should 
equal  Russia's  population  within  the  next  few  decades.  It  must  be 
remembered  in  viewing  this  chart  that  the  populations  of  the  Asiatic 
countries  (especially  the  populations  of  China  and  India)  are  not  shown 
here.  If  all  the  countries  of  the  world  were  considered,  it  would  be 
seen  at  once  that  for  many  years  to  come  there  is  no  likelihood  of  the 
United  States  having  the  greatest  population  in  the  world.  It  is  only 
because  Asiatic  countries  have  been  omitted  that  we  seem  to  be  so 
nearly  the  head  of  the  list. 


last  portion  of  Chapter  X. 
Fig.   120  contains   much 


no 

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leEo 


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INCREASE  OF  POPULATION 

IN  THE 

UNITED    STATES 

AND THE 

PRINCIPAL  COUNTRIES  OF  EUROPE 

paoM 
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leoO  I8IO  1620  1630  I640  I650  l6eO  1870  1660  1690      '    I90Q 

From  the  United  States  Statistical  Alias,  Census  of  1900 

Fig.  120.    The  Population  of  the  United  States  Compared  with  the  Population  of 
the  Principal  Countries  of  Europe  from  1800  to  1900,  Inclusive 

Written  words  requiring  one  hour  to  read  could  not  convey  as  much  information  as  this  chart  gives. 
In  considering  the  slope  of  the  curve  for  the  United  States  it  must  be  remembered  that  the  slope  of  a 
curve  does  not  indicate  the  percentage  rate  of  increase  or  decrease.  The  increasing  slope  of  the  United 
States  curve  does  not  in  itself  prove  any  increase  in  the  percentage  rate  of  growth.     Compare  Fig.  121 

130 


COMPARISON    OF    CURVES 


131 


statement  regc^x^^i^i^ 
Starting 


The  reader  should  keep  constantly  in  mind  when  viewing  Fig.  120 
that  the  slope  of  a  curve  line  crossing  a  field  ruled  with  ordinary  rec- 
tangular co-ordinate  lines  on  an  arithmetical  scale  tells  nothing  about 
the  percentage  rate  of  growth  from  period  to  period.  The  slope  of 
the  United  States  curve  is  very  much  steeper  in  the  upper  portion 
of  Fig.  120  than  in  the  lower  portion,  but  the  greater  slope  does  not 
prove  that  we  are  growing  more  rapidly  on  a  percentage  basis  than 
early  in  the  century.  The  slope  of  a  curve  plotted  on  a  natural  scale 
of  rectangular  co-ordinates  shows  only  the  size  of  the  increments  added 
from  period  to  period  and  it  tells  nothing  whatever  about  percentage 
growth. 

Fig.  121  has  been  drawn  to 
assist  in  proving  the  preceding 
arding  curve  slope, 
with  one  dollar,  it  was 
assumed  that  a  uniform  increase 
of  10  per  cent  of  the  accumu- 
lated amount  would  be  made  at 
the  end  of  each  year.  This  is  the 
same  as  though  the  dollar  were 
placed  at  10  per  cent  compound 
interest.  At  the  end  of  thirty-six 
years  it  can  be  seen  that  the  one 
dollar  has  increased  to  nearly 
thirty-one  dollars.  Though  the 
accumulated  fund  is  shown  by  a 
smooth  curve  throughout  the 
period  of  thirty-six  years,  the  curve 
is  constantly  changing  its  slope  in 
spite  of  the  fact  that  the  rate  of 
increase  remains  constant  at  10  per 
cent  per  year.  The  curve  in  Fig. 
121  is  very  similar  in  shape  to  the  curve  for  the  United  States  in  Fig. 
120.  This  similarity  in  shape  shows  conclusively  how  much  the  reader 
would  be  misled  if  he  should  assume  that  the  increasing  slope  of  the 
curve  in  Fig.  120  proved  in  itself  an  increase  in  the  rate  of  growth. 
The  actual  percentage  rate  of  the  growth  for  Fig.  120  can  best  be  stud- 
ied by  making  an  entirely  new  chart  for  the  purpose  of  observing 
percentage  rates  only. 


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Fig.  121.  Curve  Showing  the  Growth 
of  One  Dollar  at  lo  per  cent  Com- 
pound Interest  for  Thirty-six  Years 

Here  the  rate  of  increase  is  uniformly  10  per  cent 
per  year,  but  the  slope  of  the  curve  is  constantly 
changing.  The  general  shape  of  this  curve  is 
somewhat  similar  to  the  shape  of  the  population 
curve  for  the  United  States  seen  in  Fig.  120. 
The  slope  of  a  curve  plotted  on  ordinary  co- 
ordinate paper  tells  nothing  about  the  per- 
centage rate  of  growth.  See  Fig.  122  and  Fig. 
123 


132  GRAPHIC    METHODS 

*  The  ordinary  form  of  graphic  chart  plotted  on  rectangular  co- 
ordinate paper  with  the  natural  or  arithmetical  spacing  of  the  lines 
has  some  serious  limitations  which  may  cause  a  chart  to  be  misleading. 
The  true  function  of  such  a  chart  is  to  portray  comparative  fluctua- 
tions. This  desired  result  is  secured  clearly  and  satisfactorily  when 
the  factors  or  quantities  compared  are  of  nearly  the  same  value  or 
volume,  but  analysis  will  show  that  the  result  is  not  accomplished 
when  the  amounts  compared  differ  greatly  in  value  or  volume.  The 
extent  or  degree  of  the  fluctuation  as  indicated  on  the  ordinary  chart 
depends  in  a  measure  on  the  proximity  of  the  curves  to  the  top  or  bot- 
tom of  the  chart.  The  chart  registers  the  actual  change  in  the  value 
rather  than  the  ratio  or  percentage  of  change.  The  wider  the  range 
of  scale  the  greater  the  variation  between  the  actual  and  the  relative 
changes. 

This  same  criticism  applies  to  charts  which  employ  two  or  more 
scales  for  various  records  or  curves.  If  the  different  scales  are  in 
proper  proportion  the  result  is  the  same  as  with  one  scale,  but  when 
two  or  more  scales  are  used  which  are  not  proportional,  an  indication 
which  is  absolutely  false  may  be  given  with  respect  to  comparative 
fluctuation.  Charts  made  on  a  percentage  basis  are  used  to  some 
extent  in  graphic  work,  and  these  correct  the  deficiency  in  the  ordinary 
chart  by  showing  the  changes  in  the  percentages  of  increase  or  decrease. 
In  correcting  one  deficiency,  however,  another  is  introduced.  The 
percentage  scale  gives  no  clue  to  the  magnitude  of  the  quantities 
represented  by  a  curve.  The  true  proportions  of  relative  changes  are 
shown,  but  the  actual  values  are  not  indicated.  The  use  of  the  per- 
centage scale  also  requires  considerable  labor  for  computing  the  per- 
centages of  change. 

As  a  substitute  for  the  ordinary  (or  natural)  scale  and  for  the  scale 
of  percentages,  as  well  as  for  compound  scales,  the  logarithmic  scale, 
or  scale  of  ratios,  practically  meets  all  the  requirements.  The  logarith- 
mic scale  permits  the  exhibition  of  both  actual  and  relative  values 
and  actual  and  relative  fluctuations.  While  some  knowledge  of  log- 
arithms will  make  plain  certain  features  which  otherwise  are  hard  to 
understand,  no  special  knowledge  of  higher  mathematics  is  essential 
to  the  use  of  the  logarithmic  scale.  The  principles  involved  are  the 
same  as  those  embodied  in  the  slide  rule,  and  any  treatise  on  the  slide  , 

'Portions  of  this  discussion  on  charts  plotted  by  the  logarithmic  scale  are  adapted  from  an  article  by  W.  J.  Cunningham, 
in  the  Railway  Age  Gazette,  June  25,  1909. 


COMPARISON    OF    CURVES  133 

rule  will  make  them  sufficiently  clear.  A  person  who  can  plot  a  chart 
to  the  ordinary  scale  should  have  no  difficulty  in  using  the  logarithmic 
scale. 

No  matter  what  the  location  on  the  chart,  if  the  logarithmic 
spacing  is  used  on  the  vertical  scale,  for  curves,  the  angle  of  the  upward 
or  downward  inclination  is  the  same  for  all  curves  affected  by  the 
same  percentage  of  change.  Curves  having  an  increase  equaling 
the  distance  from  100  to  200,  200  to  400,  300  to  600  (or  the  distance 
between  any  number  on  the  scale  and  double  that  number)  have  an 
increase  of  100  per  cent  and  show  the  same  slope.  It  will  be  noticed, 
for  instance,  from  any  paper  ruled  logarithmically,  or  from  Fig.  123, 
that  the  distance  on  the  logarithmic  scale  from  10  to  20  is  the  same 
as  from  200  to  400. 

In  Fig.  122,  we  have  curves  plotted  for  comparative  study  in  the 
manner  most  convenient  when  ordinary  arithmetically  ruled  cross- 
section  paper  is  used.  Some  of  these  curves  represent  large  quantities, 
so  that  they  are  on  the  upper  portion  of  the  chart,  while  others  rep- 
resent comparatively  small  quantities  and  fall  near  the  bottom  of  the 
chart. 

Just  because  the  curves  in  the  upper  portion  of  the  chart  represent 
numerically  larger  quantities,  they  have  much  more  vertical  movement 
up  and  down  on  the  face  of  the  chart  than  those  curves  in  the  lower 
portion  of  the  chart  which  may  have  an  even  greater  amount  of  per- 
centage fluctuation.  This  wide  difference  in  the  amount  of  vertical 
movement  on  a  page  is  one  unfortunate  source  of  confusion  to  persons 
who  are  just  beginning  to  study  curve  charting. 

Fig.  123  is  plotted  from  the  same  data  as  Fig.  122,  but  it  is  on 
paper  having  logarithmic  spacing  for  the  vertical  scale  with  the  ordi- 
nary arithmetical  spacing  for  the  horizontal  scale.  With  the  logarith- 
mic spacing  on  the  vertical  scale  the  fluctuations  in  the  different 
curves  show  in  true  proportion.  Curve  F  appeared  insignificant  in 
Fig.  122  because  it  happened  to  fall  near  the  bottom  of  the  chart 
where  percentage  fluctuations  are  not  prominently  shown.  In  Fig. 
123,  however,  curve  F  shows  up  as  having  far  the  greatest  percentage 
changes  of  any  curve  on  the  whole  chart.  For  persons  who  under- 
stand even  slightly  the  principles  involved  in  reading  charts  plotted 
on  logarithmic  paper.  Fig.  123  shows  up  the  facts  in  much  more  con- 
venient form  than  Fig.  122.  To  make  comparison  most  convenient, 
the  two  figures  are  placed  on  facing  pages,  134  and  135. 


134 


GRAPHIC   METHODS 


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W.  J.  CunrAngham,  in  the  Railway  Age  Gazette 


Fig. 


122.  Passengers  and  Employees  Killed  and  Injured 
in  Train  Accidents  for  All  Railroads  in  the  United 
States.  (From  Quarterly  Reports  of  the  Interstate 
Commerce  Commission) 

Curve  A.     Passenger  miles  (2000  on  scale  equals  20  billion  passenger 

miles) 
Curve  B. 
Curve  C. 
Curve  D. 
Curve  E. 
Curve  F. 


1 


Ton  miles  (2000  on  scale  equals  20  billion  ton  miles) 

Number  of  employees  injured 

Number  of  passengers  injured 

Number  of  employees  killed 

Number  of  passengers  killed 
Compare  this  chart  with  Fig.  123.  The  data  plotted  here  by  the  or- 
dinary natural  scale  of  co-ordinates  are  replotted  in  Fig.  123,  using 
logarithmic  co-ordinates.  Note  the  peak  in  1904  in  Curve  D. 
The  number  of  passengers  injured  was  approximately  doubled  in  a 
short  period  of  time.  In  the  same  period  of  time  the  number  of 
passengers  killed  increased  to  seven  times  what  it  had  been,  yet  the 
peak  on  Curve  F  does  not  attract  great  attention.  Notice  these  same 
peaks  in  Fig.  123  with  the  logarithmic  scale 

It  is  unfortunate  that  there  is  so  much  difficulty  in  obtaining 
paper  having  the  logarithmic  ruling  in  one  direction  and  the  arith- 
metical ruling  in  the  other  direction.  The  arithmetical  ruling  in  one 
direction  is  essential  for  statistical  work,  since  we  must  ordinarily 
plot  as  one  scale  data  representing  years  or  other  subdivisions  of 
time.  In  statistical  work  we  cannot  well  use  a  paper  having  logarith- 
mic ruling  in  both  directions,  yet  that  is  the  only  kind  of  logarithmic 
paper  which  can  be  obtained  from  most  stores  selling  drawing  materials 


COMPARISON    OF    CURVES 


135 


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Fig.  123.  Passengers  and  Employees  Killed  and  Injured 
in  Train  Accidents  for  All  Railroads  in  the  United 
States.  (From  Quarterly  Reports  of  the  Interstate 
Commerce  Commission) 


Curve  A. 
miles) 
Curve  B. 
Curve  C. 
Curve  D. 
Curve  E. 
Curve  F. 


Passenger  miles  (2000  on  scale  equals  20  billion  passenger 


Ton  miles  (2000  on  scale  equals  20  billion  ton  miles) 

Number  of  emploj^ees  injured 

Number  of  passengers  injured 

Number  of  employees  killed 

Number  of  passengers  killed 
This  illustration  is  a  replot  of  Fig.  122  by  using  the  logarithmic  scale  in 
the  vertical  direction.  In  reading  a  chart  in  which  a  logarithmic 
vertical  scale  is  used,  attention  may  be  given  to  the  slope  of  the  curve 
lines.  Curves  having  the  same  slope  upwards  or  downwards  have 
the  same  percentage  change.  Note  that  curves  with  a  logarithmic 
scale  do  not  have  zero  for  the  bottom  line  of  the  chart.  It  is,  how- 
ever, desirable  to  have  the  bottom  line  either  at  ten  or  some  power 
of  ten  on  the  vertical  scale 

and  engineering  supplies.  A  person  doing  statistical  work  for  which 
paper  with  the  logarithmic  ruling  is  desirable  may  occasionally  have  to 
rule  his  own  paper.  This,  however,  Is  not  an  impossible  task  especially 
if  one  has  a  slide  rule.  The  spacing  of  the  lines  can  be  copied  from 
either  scale  of  the  slide  rule,  or  it  may  be  worked  out  easily  to  fit  any 


136 


GRAPHIC    METHODS 


given  space  by  dividing  into  tenths  and  hundredths  and  using  tables  I 
of  logarithms. 

It  is  of  interest  to  note  here  that  the  data  of  Fig.  121  would  show 
as  a  perfectly  straight  line  if  plotted  on  paper  having  the  logarithmic 
mling  for  the  vertical  scale.  Since  the  increase  from  year  to  year  is 
uniform,  on  a  percentage  basis,  the  points  of  the  curve  all  fall  on  a 
straight  line  drawn  from  the  first  point  to  the  last  point. 


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W.  J.  Cunningham  in  Proceedings  of  New  England  Railroad  Club 

Fig.  124.    Book  Value  of  Material  on  Hand  for  a  Large  Eastern  Railroad 

The  logarithmic  scale  is  particularly  valuable  for  an  operating  chart  such  as  this  when  there  is  a  great  differ- 
ence in  the  size  of  the  figures  which  must  be  compared.  The  lower  curve  here  averages  about  $60,000 
while,  the  upper  curve  averages  about  $1,100,000.  The  logarithmic  scale  permits  accurate  comparison 
of  various  curves  to  determine  whether  any  curves  are  out  of  harmony  with  the  other  curves 

Fig.  124  gives  an  especially  interesting  use  of  curves  on  the  log- 
arithmic ruling.  Executives  who  have  puzzled  over  methods  for 
•controlling  the  quantity  of  materials  or  supplies  on  hand  realize  full 
well  that  it  is  sometimes  just  as  important  to  watch  the  curves  for 
materials  having  only  a  relatively  small  consumption  as  it  is  to  watch 
the  curves  for  those  materials  of  which  the  greatest  quantity  is  used. 
The  mere  fact  that  great  amounts  of  capital  are  tied  up  in  stocks 
of  certain  largely  used  materials  tends  in  itself  to  cause  very  careful 
scrutiny  of  those  accounts,  while  numerous  small  or  inactive  accounts 
may  be  entirely  overlooked  or  neglected.  A  little  study  often  shows 
that  there  is  no  necessity  for  carrying  so  much  material  on  hand. 


I 


COMPARISON    OF    CURVES  137 

If  charts  similar  to  Fig.  124  are  used,  the  executive  can  tell  instantly 
whether  the  stocks  in  different  departments  or  of  different  kinds  of 
material  are  increasing  or  decreasing  simultaneously  and  propor- 
tionately. 

"To  summarize — with  the  ordinary  arithmetical  scale,  fluctuations 
in  large  factors  are  very  noticeable,  while  relatively  greater  fluctua- 
tions in  smaller  factors  are  barely  apparent.  The  logarithmic  scale 
permits  the  graphic  representation  of  changes  in  every  quantity  with- 
out respect  to  the  magnitude  of  the  quantity  itself.  At  the  same 
time,  the  logarithmic  scale  shows  the  actual  value  by  reference  to  the 
numbers  in  the  vertical  scale.  By  indicating  both  absolute  and  rela- 
tive values  and  changes,  the  logarithmic  scale  combines  the  advantages 
of  both  the  natural  and  the  percentage  scale  without  the  disadvantages 
of  either," 


Chapter  VIII 


COMPONENT  PARTS  SHOWN  BY  CURVES 


show  the  changes 
as  time  goes 


IN  Chapter  I  various  examples  were  given  in  which  the  component 
parts  or  factors  making  up  a  complex  whole  were  shown  in  their 
relative    sizes.      It   frequently   happens   that    it    is    necessary  to 
J3V.0  which  occur  in  the  size  of  different  components 
on.     In   this   chapter  we  shall   consider  only  examples 
of  charts  showing   the  fluctuating    size,  at  different  times,  of    com- 
ponents which  make  up  a  total  of  100  per  cent. 

In  Fig.  125  the 
proportionate  num- 
ber, voltage,  and 
candle-power  of 
various  types  of 
standard  incandes- 
cent lamps  delivered 
in  different  years  by 
the  New  York  Edi- 
son Co.  are  shown 
in  a  series  of  vertical 
bars  which  are  all  of 
the  same  length, 
representing  100  per 
cent.  No  statement 
is  made   or  implied 


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New  York  Edison  Company 

Fig.  125.  The  Number,  Voltage,  and  Candle-Power  of  the 
Different  Types  of  Standard  Incandescent  Lamps 
DeUvered  by  the  New  York  Edison  Company  in 
Different  Years,  Shown  as  a  Percentage  of  the  Totals 
of  All  Lamps  Delivered 

The  chart  was  drawn  in  four  contrasting  colors  and  was  framed  for  a 
wall  exhibit 


in  regard  to  the  total 
figures,  which  may 
have  increased  or 
decreased  from  year 
to  year.  All  we  are 
interested  in,  in  this  chart,  is  the  proportion  of  the  different  components 
which  in  their  aggregate  make  up  the  bar  representing  100  per  cent 
in  any  year. 

In  Fig.  126  the  total  height  of  the  chart  represents  100  per  cent. 

138 


COMPONENT  PARTS  SHOWN  BY  CURVES 


139 


Per  Cent 

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80 
70 
60 
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50  50 

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20  80 

10  90 


18EO 


o   100 


1830 


1840 


1850 


I860 


t670 


1880 


1890 


1900 


Fig.  126.    Percentage  of  United  States  Foreign  Trade  Carried  in  American  Vessels 
and  in  Foreign  Vessels  by  Decades,  1820  to  1900 

This  type  of  chart  requires  a  more  highly  educated  reader  than  the  type  of  chart  shown  in  Fig.  125,  but  it 
gains  by  making  the  information  stand  out  more  clearly  than  possible  with  a  series  of  bars 

To  show  that  the  chart  is  absolutely  limited  to  the  height  represent- 
ing 100  per  cent,  we  use  a  broad  line  for  the  zero  line  and  another 
broad  line  at  the  top  for  the  100  per  cent  line.  Instead  of  showing 
the  percentages  at  different  decades  by  the  method  of  shaded  bars 
used  in  Fig.  125,  the  vertical  lines  representing  decades  are  first  marked 
with  points  dividing  the  lines  into  component  parts,  then  the  points 
on  the  various  lines  are  joined  to  give  a  curve.  The  area  under- 
neath the  curve  is  shaded  in  this  illustration  simply  to  give  a  great- 
er contrast  between  the  two  portions  of  the  chart.  Charts  of  this 
kind  made  with  shaded  or  colored  areas  are  understood  by  a  sur- 
prisingly large  number  of  people  who  ordinarily  would  not  under- 
stand a  chart  made  by  using  curve  lines  without  the  shaded  or  col- 
ored areas. 

The  double  scale  at  the  right  of  Fig.  126  is  worth  noting.  The 
percentage  for  the  United  States  can  be  read  for  any  decade.  The 
percentage  for  foreign  vessels  can  also  be  read  for  any  decade  by  using 
the  reversed  scale,  in  which  zero  is  placed  at  the  top  and  100  per  cent 
at  the  bottom.  Though  a  double  scale  is  scarcely  necessary  on  a 
chart  as  simple  as  Fig.  126,  it  is  frequently  desirable  to  have  a  double 
scale. 

Another  very  striking  wall  chart  Is  shown  in  Fig.  127.  Here  as 
in  Fig.  125  the  chart  was  framed,  but  the  frame  shows  in  the  photo- 
graph only  as  a  black  border.     In  making  up  this  chart  co-ordinate 


140 


GRAPHIC    METHODS 


paper  was  used  for  a  background.  The  upper  half  of  the  chart  shows 
the  24  hours  of  the  day  divided  between  hours  of  darkness,  hours  of 
twihght  and  cloudiness,  and  hours  of  sunshine,  totaling  100  per  cent 
for  each  month  in  the  year.  The  hours  of  darkness  are  definitely 
known  from  almanac  figures  and  can  be  plotted  as  a  smooth  curve. 


New  Yort  Edison  Company 

Fig.  127.  Industrial  Accidents  in  Different  Months 
of  the  Year  Compared  with  the  Hours  of  Sun- 
light Each  Day  in  Different  Months  According 
to  Weather  Records  for  New  York  City  in  1 9 1  o 

Twenty-four  hours  in  a  day  are  shown  as  100  per  cent  divided 
between  darkness,  semi-darkness,  and  sunshine.  Curves 
showing  accidents  for  three  different  years  have  the  same 
general  shape  as  the  upper  curve  representing  hours  of  dark- 
ness. The  scale  for  the  accident  curves  should  have  been 
started  so  as  to  show  zero  at  the  bottom  of  the  curve  field 

The  hours  of  cloudy  weather,  however,  vary  in  different  years.  The 
area  showing  cloudiness  and  twilight  was  drawn  from  actual  weather 
observations  made  in  New  York  City  during  the  year  1910.  The  per- 
centage of  sunshine  in  different  months  fluctuates  considerably,  as 
will  be  noticed  in  the  chart. 


COMPONENT  PARTS  SHOWN  BY  CURVES  141 

The  lower  half  of  Fig.  127  contains  three  curves  showing  the 
monthly  distribution,  for  three  successive  years,  of  about  700  deaths 
annually  from  industrial  accidents  reported  from  an  area  embracing 
80,000  plants.  The  similarity  of  these  curves,  showing  the  number 
of  fatal  accidents  per  month,  to  the  curves  showing  the  percentage  of 
darkness,  is  intended  to  convey  to  the  person  seeing  the  wall  exhibit, 
the  truth  of  the  statement  at  the  top  of  the  chart,  that  "an  abundance 
of  light  tends  to  prevent  industrial  accidents."  Though  Fig.  127  is 
a  very  commendable  and  effective  piece  of  work,  it  should  be  pointed 
out  that  there  is  danger  of  exaggerating  the  facts  in  the  way  in  which 
the  chart  is  prepared.  The  lower  left-hand  scale  does  not  begin  at 
zero.  By  measuring,  it  can  be  seen  that  the  scale  begins  at  20  acci- 
dents per  month.  The  bottom  line  of  the  curve  field  should  have 
been  drawn  near  the  edge  of  the  picture  frame  to  represent  zero. 
This  change  in  the  bottom  line  would  have  given  the  reader  a  more 
accurate  idea  of  the  increase  of  deaths  in  those  months  having  the 
greatest  proportion  of  darkness.  This  chart  really  does  not  exaggerate 
the  facts  seriously,  for  the  three  curves  for  deaths  and  the  curve  for 
darkness  would  really  be  of  approximately  the  same  shape  even  if 
the  zero  line  had  been  shown  in  its  correct  position.  Yet  it  is  a  fact 
that  the  omission  of  the  full  scale  in  the  chart  may  cause  a  person 
glancing  hastily  at  the  chart  to  distrust  it  simply  because  the  zero 
line  is  not  shown. 

In  Fig.  128  a  number  of  different  components  are  shown  to  make 
up  a  total  of  100  per  cent.  This  type  of  chart  is  especially  good  to 
give  instantly  a  general  idea  of  the  relative  size  of  the  components 
or  factors  which  enter  into  any  total,  and  to  show  the  changes  in  these 
factors  as  time  goes  on.  Though  it  is  fairly  easy  to  see  in  Fig.  128 
what  the  changes  are  which  have  occurred  in,  say,  the  item  for  "Gen- 
eral" expenses,  it  is  not  at  all  easy  to  determine  the  changes  which 
have  occurred  in  the  item  for  "Conducting  Transportation."  The 
eye  cannot  measure  correctly  the  increase  or  decrease  in  width  of  any 
area  as  great  as  that  representing  the  item  for  "Conducting  Trans- 
portation," especially  if  there  is  no  straight  line  to  gauge  by,  either 
at  the  top  or  the  bottom  of  the  area  under  consideration. 

Though  the  method  of  presenting  the  facts  in  Fig.  128  is  excellent 
to  give  a  rough  general  idea  or  to  reach  unskilled  readers,  the  method 
of  presenting  the  facts  in  Fig.  129  is  likely  to  give  the  more  accurate 
impression.     In  Fig.   129,  each  of  the  different  expense  accounts  is 


142 


GRAPHIC    METHODS 


100 


plotted  as  a  separate  curve  measured  from  zero  as  a  base  line.  It  can 
be  seen  at  once  in  Fig.  129  that  the  component  for  "Conducting 
Transportation"  increased  rapidly  until  1895,  ran  along  fairly  uniformly 
to  1900,  then  slightly  decreased,  then  increased  again.  By  having 
each  curve  plotted  separately  with  the  points  measured  from  a  zero 
base  line,  the  eye  can  judge  instantly  and  accurately  the  changes 
which  have  occurred  over  a  period  of  years  in  any  component  \\'hich 
enters  into  the  total.  In  an  illustration  like  Fig.  129  it  should  be 
Percent  shown    in   the   title, 

or  preferably  on  the 
chart  itself,  that  the 
sum  of  the  heights 
of  all  the  curves 
given  on  the  chart  is 
constantly  100  per 
cent  as  indicated  by 
the  broad  line  at  the 
top  of  the  chart. 
The  reader  will  then 
know  that  if  any  one 
curve  on  the  chart 
goes  up,  some  other 
curve  or  curves  must 
come  down  in  order 
that  the  100  per  cent 
line  may  remain 
straight  and  hori- 
zontal. 


Adapted  from  Railway  Age  Gazette 

Fig.  128.     Percentage  Distribution  of  the  Expenses  of 
Operating  the  Railroads  of  the  United  States 

Here  a  number  of  dijferent  factors  enter  into  the  total  100  per  cent. 
Since  the  strips  representing  different  expenses  vary  at  both  top  and 
bottom,  it  is  not  easy  to  see  from  year  to  year  how  much  any  strip 
may  be  increasing  or  decreasing.     Compare  with  Fig.  129 


Fig.  130  is  an  interesting  application  of  the  method  of  using  areas 
to  show  components  with  100  per  cent  shown  as  a  straight  line  at  the 
top  of  the  combined  area.  As  in  this  case  a  large  part  of  the  con- 
struction work  was  finished,  the  actual  number  of  accidents  in  the 
construction  department  dropped  to  almost  nothing,  and,  because 
the  shaded  area  for  construction  grew  less,  it  w^as  necessary  that  the 
other  areas  should  widen  out  if  the  100  per  cent  line  at  the  top  were 
to  remain  a  straight  line.  Here  the  weak  point  in  the  method  of 
charting  is  the  same  as  that  indicated  for  Fig.  128.  The  person  ob- 
serving the  chart  has  no  way  of  telling  whether  the  factors  included 
in  the  100  per  cent  have  grown  less  or  grown  greater,  and  whether 


COMPONENT  PARTS  SHOWN  BY  CURVES 


143 


Percent 
loo 


the  quantities  represented  by  the  different  areas  have  changed  in 
actual  size  or  only  in  relative  size.  Where  great  fluctuations  occur 
from  time  to  time  and  many  factors  enter  into  the  total,  it  is  best 
to  draw  charts  in  the  form  of  Fig.  129  with  a  conmion  zero  line,  or  in 
the  form  of  Fig.  131,  where  each  factor  has  its  own  separate  base  line, 
or  in  the  form  of  Fig.  132  and  Fig.  133,  in  which  the  lines  on  the  chart 
represent  actual  quantities  rather  than  percentages  of  an  aggregate  or 
total  sum. 

Note  in  Fig.  130  and  Fig.  131  the  Sl^-inch  by  11-inch  co-ordinate 
paper  on  which  the  ruling  is  so  arranged  that  the  paper  may  be  used 
for  almost  any  subdivisions  of  time,  such  as  days,  weeks,  months, 
etc.,  as  seen  in  Figs. 
57, 103. 131, 134,  and 
156. 

In  Fig.  130  the 
paper  was  used  for  a 
time-scale  of  three 
years  by  months, 
the  total  height  of 
the  chart  being  put 
at  100  per  cent,  us- 
ing fifty  out  of  the 
fifty-two  spaces  on 
the  paper.  Fifty -two 
spaces,  correspond- 
ing to  the  number  of 
weeks  in  a  year,  of 
course  are  necessary 
when  the  paper  is 
used  to  represent 
weeks  on  the  long 
dimension  of  the 
sheet. 

Fig.  131  and  Fig.  130  depict  exactly  the  same  data.  In  Fig.  131 
the  facts,  which  in  Fig.  130  were  represented  by  areas,  are  shown  as 
separate  curves,  each  cui've  with  its  own  base  line.  Having  this  series 
of  separate  curves  on  one  sheet  of  paper  permits  an  executive  to  com- 
pare the  number  of  accidents  in  one  department  with  the  number 
of  accidents  in  any  other  department  at  any  one  time,  or  to  study 


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Fig. 


129.  Percentage  Distribution  of  the  Expenses  of 
Operating  the  Raihroads  of  the  United  States.  The 
Combined  Height  of  All  the  Curves  Shown  Equals 
100  Per  Cent  on  the  Scale 

This  illustration  represents  the  same  data  as  Fig.  128.  Here  the  per- 
centage for  each  expense  is  read  from  the  zero  base  line  instead  of 
from  one  to  the  other  of  the  fluctuating  lines  on  either  side  of  an 
area.  This  method,  though  not  so  popular  as  the  method  of  Fig.  128, 
permits  more  accurate  reading 


144 


GRAPHIC   METHODS 


O 


number  of  accidents  occurring  in  each  department,  as 
PERCEJTTAGES  OF  THE  TOTAL. 
12  Months  Averages. 


^ercenl 


''*9!!J?3'~'*^'^^'*''^'**®^C>HNHNI0^U3«0t-a3OOHWHNWTj<U»«06-00 
nt-ii-i  HHiH  H  H  H 

1910-11  1911-lE  1912-13 


Fig.  130.    Percentage  of  Accidents  Occurring  in  Each  Department  of  a  Large  Industrial 
Plant.     Plotted  Monthly  by  Twelve-month  Averages 

By  this  method,  with  a  constant  width  to  represent  100  per  cent,  any  great  change  in  any  component 
affects  all  other  components.  Here  the  decrease  in  construction  accidents  causes  the  areas  depicting 
other  accidents  to  increase  in  width,  even  though  there  may  be  no  increase  in  the  actual  number  of 
accidents.     Compare  Fig.  131 

This  cut  was  made  from  specially  ruled  co-ordinate  paper  8j^  inches  by  11  inches,  with  all  lettering  done  by 
typewriter.  The  ruling  as  used  here  shows  100  per  cent  and  three  years  by  months.  Note  also  Figs.  57, 
103,  134  and  1.56,  for  which  this  .same  universal  ruling  has  been  used 


COMPONENT  PARTS  SHOWN  BY  CURVES 


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ririni                                             Hr-IH                                              Hrint 

1910-11                          1911-12                            1912-13 

Fig.  131.    Actual  Number  of  Accidents  Occurring  in  Each  Department  of  a  Large 
Industrial  Plant.    Plotted  Monthly  by  Twelve-month  Averages 

In  this  chart  the  actual  condition  in  each  department  can  be  seen  much  more  clearly  than  by  the  method 
used  in  Fig.  130.  Here  each  department  is  judged  by  its  own  record  without  danger  of  unjust  criticism 
based  on  conditions  in  other  departments 

For  a  more  complete  discussion  of  Figs.  130  and  131  and  of  the  contrast  of  methods  followed  in  preparing 
them  the  reader  is  referred  to  pages  142,  143  and  146 


146 


GRAPHIC    METHODS 


the  fluctuations  in  the  accidents  of  any  one  department  over  a  long 
period  of  time. 

As  accidents  never  occur  with  any  regularity,  curves  representing 
the  actual  number  of  accidents  are  likely  to  fluctuate  a  great  deal. 
There  was  such  variation  in  the  different  months  for  the  number  of 
accidents  represented  in  Figs.  130  and  131  that  it  was  almost  im- 
possible to   draw   any  definite  conclusion  from   curves  for  monthly 


New  York  Edison  Company 


Fig. 


data, 
basis 


132.    Nature  of  the  Electrical  Load  Connected  to  the  System 
of  the  New  York  Edison  Company,  1893  to  1912 

In  the  preceding  illustrations  100  per  cent  was  indicated  by  a  straight  line  at  the 
top  of  the  chart.  Here  the  line  representing  100  per  cent  is  a  curve.  Though 
the  actual  sizes  of  different  components  can  be  seen  by  this  method,  percentages 
can  only  be  estimated  from  the  widths  of  the  areas.  The  scale  for  this  type  of 
chart  must  read  in  actual  quantities  rather  than  in  percentages.  On  this  wall 
exhibit  the  scale  has  been  omitted  entirely 

The  data  for  Fig.  130  and  for  Fig.  131  were  plotted  on  the 
of  giving,  monthly,  the  average  number  of  accidents  in  each 
department  during  the  last  twelve  months  for  which  records  were 
available.  Actual  figures  in  tabulated  form  were  used  to  show  for 
immediate  reference  the  number  of  accidents  in  any  month.  The 
curves  on  the  twelve-months  average  basis  were  consulted  to  deter- 
mine whether  there  was  any  great  increase  or  decrease  in  any  de- 
partment. 

In  Fig.  132  the  vertical  scale  was  omitted,  perhaps  with  the  idea 
that  the  chart  would  thus  appear  more  simple  to  the  average  indi- 


COMPONENT    PARTS    SHOWN    BY    CURVES 


147 


vidual  attending  a  large  exhibition.  If  the  scale  were  given,  however, 
it  would  be  plotted  on  the  basis  of  actual  horse-power  rather  than 
on  percentage,  for  the  top  curve  here  represents  the  total  quantity. 
Percentage  scales  cannot  well  be  used  in  diagrams  of  component  parts 
if  a  fluctuating  curve  line  instead  of  a  horizontal  line  representing 
100  per  cent  is  given  at  the  top.  The  reader  may,  however,  get  a 
fair  idea  of  the  percentages  if  he  roughly  calculates  the  height  of  the 
areas  in  question  on  any  vertical  line  of  the  co-ordinate  ruling  and 
then,  using  that  vertical  line  as  a  measuring  rod,  estimates  the  height 
of  the  areas  as  a  percentage  of  the  total  height  of  the  chart. 

In  Fig.  133  the  straight  line  at  the  top  of  the  chart  does  not  have 
any  significance,  as  it  is  due  only  to  the  co-ordinate  ruling  which 
serves  as  a  background  to  the  chart  itself.  The  important  part  of  the 
chart  ends  at  the  top  of  the  shaded  area.  We  may  consider  the  top 
of  the  whole  shaded  area  as  a  curve  and  read  the  values  accordingly 
from  the  scales  on  the  right-  and  left-hand  sides.  In  fact,  any  curve 
on  the  whole  chart  may  be  considered  as  a  sub-total,  which  includes 
all  of  those  components  or  factors  shown  as  separate  areas  beneath 
that  curve.  Thus  the  "Total  Shop  Cost"  includes  all  those  com- 
ponents shown  below  the  *' Total  Shop  Cost"  curve. 


Jan 


Apr 


May 


July 


Aug         Sept 


Nov 


Dec 


Adapted  from  Factory 


Fig.  133.    Factors  Entering  into  the  Total  Costs  and  Estimated  Value  of  the  Product 

of  a  Manufacturing  Plant 

The  vario'js  elements  entering  into  total  shop  cost  are  plotted,  each  built  up  on  the  areas  below.  The 
"Estimated  Valuation"  is  based  upon  market  prices  for  the  finished  goods.  Vertical  distances  between 
the  "Total  Cost"  curve  and  the  "Estimated  Valuation"  curve  show  the  estimated  profit.  Note  the 
use  of  dimension  lines  in  combination  with  the  scales 


148  GRAPHIC    METHODS 

The  use  of  engineering  dimension  lines  in  Fig.  133  is  of  interest, 
for  the  dimension  hnes  add  considerably  to  the  clearness  of  the  drawing. 
In  the  center  of  the  chart  the  vertical  dimension  lines  on  both  sides 
of  the  names  for  each  area  show  distinctly  that  the  chart  must  be 
read  on  the  basis  of  the  vertical  distance  between  the  two  curves  on 
either  side  of  any  area.  At  the  right-  and  left-hand  edges  of  the  chart 
the  over-all  dimension  lines  show  the  reader  at  once  how  to  read  the 
chart  so  as  to  include  all  the  various  components  entering  into  any 
total  which  may  be  under  consideration.  The  use  of  dimension  lines 
should  be  thoroughly  understood  by  everyone  drawing  charts  or 
plotting  curves,  and  by  everyone  having  graphic  presentations  to 
read.  Dimension  lines  may  add  much  to  the  clearness  of  a  chart 
without  being  in  themselves  unduly  conspicuous. 


Chapter  IX 
CUMULATIVE  OR  MASS  CURVES 

THE  curves  thus  far  shown  have  practically  all  been  of  a  type 
in  which  the  thing  plotted  was  a  value  or  a  rate  per  week,  per 
month,  or  per  year.  The  tendency  of  such  curves  is  to  follow 
a  horizontal  direction  unless  affected  by  conditions  which  cause  sea- 
sonal fluctuations  or  gradual  increases  or  decreases.  In  this  chapter 
we  shall  consider  curves  in  which  the  data  plotted  concern  total  out- 
put, rather  than  the  rate  of  output.  With  cumulative  or  mass  curves, 
such  as  are  considered  here,  each  point  on  the  curve  represents  a  total 
output  up  to  the  time  for  which  the  last  point  is  plotted.  The  figure 
for  each  successive  period  of  time  is  added  to  the  total  already  re- 
corded, and  the  new  total  point  is  plotted.  Because  the  figures  re- 
lating to  the  last  unit  of  time  are  always  added  to  the  total  figures 
already  recorded,  curves  of  this  type  are  called  cumulative  curves  or 
mass  curves.  The  tendency  of  a  cumulative  curve  is  to  start  at  the 
lower  left-hand  corner  of  the  co-ordinate  ruling  and  move  toward 
the  upper  right-hand  corner  of  the  sheet,  according  to  the  scale  which 
may  have  been  selected. 

Fig.  134  is  a  half-tone  illustration  of  a  cumulative-curve  chart 
representing  the  output  of  an  automobile  factory  for  one  fiscal  year 
of  the  business.  In  a  conference  between  the  sales,  engineering,  and 
manufacturing  heads  of  this  business,  it  was  decided  that  the  quantity 
of  automobiles  desired  was  fifty  per  week  until  the  first  of  April,  then 
sixty  per  week  until  the  first  of  June,  and  seventy  per  week  there- 
after, giving  a  total  production  of  three  thousand  two  hundred  auto- 
mobiles for  the  whole  season.  It  was  thought  that  the  rate  of  pro- 
duction on  the  new  model  automobile  could  be  increased  after  the 
factory  had  been  put  into  thoroughly  good  running  shape,  and  the 
schedule  rate  of  production  was  accordingly  increased  gradually  in 
the  manner  shown.     On  account  of  the  delay  in  getting  drawings 

149 


150 


GRAPHIC   METHODS 


o  o 


Factory  Schedule  and  Actual  Output 


o 


Fig.  134.    Production  Schedule  and  Actual  Output  of  an  Automobile  Factory  for 

One  Year 

The  schedule  is  shown  by  the  straiglit  lines  drawn  according  to  the  desired  output  per  week.  Actual 
output  is  indicated  by  the  waving  line  showing  at  any  date  the  total  number  of  autos  shipped  since  the 
beginning  of  the  year.  Note  the  co-ordinate  paper  of  letter-sheet  size  and  the  scheme  for  marking  off 
weeks  and  months  so  that  any  fiscal  year  may  be  shown  on  this  standard  ruled  paper 

from  the  engineering  department,  the  factory  was  able  to  ship  prac- 
tically no  cars  during  the  month  of  January,  though  the  schedule 
shows  that  one  hundred  and  fifty  cars  should  have  been  made  that 
month.  During  February,  the  factory  produced  cars  but  fell  further 
behind  schedule  constantly,  as  can  be  seen  by  the  difference  between 
the  angle  of  the  schedule  line  for  February  and  the  angle  of  the  actual 
output  line  for  February. 

It  must  be  remembered  that  with  cumulative  curves  the  angle 
between  the  curve  and  the  horizontal  line  gives  the  rate  of  production 
per  unit  of  time..  The  angle  of  the  curve  on  the  page  gives  much 
valuable  information  to  the  reader.  It  is  for  this  reason  that  cumu- 
lative curves  are  sometimes  much  more  useful  than  curves  in  which 
the  rate  of  output  is  plotted  horizontally  from  time  to  time.  In  the 
cumulative  curve  the  total  output  is  plotted,  and  changes  in  the  rate 


CUMULATIVr;    CURVES  151 

of  output,  judged  by  the  angle  of  the  curve  at  different  times,  may 
be  seen  very  easily. 

During  ^Nlarch  the  output  curve  took  a  rapid  upward  turn  and  we 
can  see  from  its  angle  that,  until  the  end  of  the  first  w^eek  in  April, 
the  output  curve  gradually  approached  the  curve  for  schedule.  During 
the  latter  part  of  March  the  factory  not  only  got  out  its  quota  of 
cars  each  week  but  produced  more  than  its  quota,  making  up  a  little 
for  the  distance  it  fell  behind  during  the  first  part  of  the  year.  Owing 
to  a  lack  of  material,  because  of  a  fire  in  a  factory  which  supplied  the 
crank  shafts  for  the  automobiles,  not  a  single  automobile  could  be 
shipped  during  the  second  week  in  April  and  only  a  few  in  the  third 
week  of  April.  The  automobile  factory  was  busy,  however,  accumu- 
lating a  large  suppty  of  parts  and  assembling  automobiles  as  com- 
pletely as  it  was  possible  to  do  without  the  crank  shafts  which  were 
lacking.  By  measuring  the  vertical  distance  between  the  output 
curve  and  the  schedule  curve,  it  will  be  seen  that  the  factory  was 
furthest  behind  its  schedule  during  the  first  week  in  May,  which  is 
one  of  the  best  automobile-selling  months  of  the  year.  If  we  count 
the  squares  between  the  output  curve  and  the  schedule  curve  we  see 
that  the  factory  Avas  about  four  hundred  and  twenty  automobiles  be- 
hind schedule  at  the  end  of  the  first  week  in  May.  As,  however,  a 
large  supply  of  parts  and  of  nearly  completed  automobiles  accumu- 
lated while  the  crank  shafts  were  delayed,  the  factory  was  able  to 
assemble  and  ship  cars  very  rapidly  when  the  crank  shafts  were  finally 
received  from  a  new  source  of  supply.  The  factory  turned  out  much 
more  than  fifty  cars  per  week  during  the  latter  part  of  May  and  was 
rapidly  catching  up  with  the  schedule,  until  the  supply  of  accumulated 
parts  was  used  up  and  the  assembling  departments  were  limited  to 
the  rate  at  which  parts  could  be  produced  in  the  machine  shop.  By 
making  every  possible  effort  in  the  machine  shop,  the  weekly  rate  of 
seventy  sets  of  parts  was  exceeded,  and  the  curve  shows  that  during 
June  and  July  the  rate  of  shipping  automobiles  exceeded  the  schedule 
rate  to  such  an  extent  that  by  the  end  of  the  third  week  the  factory 
had  caught  up  with  the  schedule  production  asked  for  by  the  sales 
department.  There  was,  however,  a  slump  in  the  factory  output  about 
the  first  of  August,  and  it  was  not  until  the  middle  of  August  that  the 
factory  was  able  to  furnish  the  desired  quota  of  automobiles  regularly. 

A  conference  held  between  the  sales  manager  and  the  factory 
manager  in  September  resulted  in  a  statement  from  the  sales  manager 


152  GRAPHIC    METHODS 

to  the  effect  that  he  could  sell  all  the  automobiles  that  the  factory 
could  produce  by  the  end  of  the  year.  The  factory  manager  was  told 
to  go  ahead  as  fast  as  he  wished  and  turn  out  all  the  cars  he  could 
up  to  a  total  of  three  thousand  five  hundred  cars.  The  schedule  line 
was  accordingly  changed  from  the  second  week  in  October,  by  drawing 
the  line  so  that  it  came  out  at  three  thousand  five  hundred  cars  at 
the  end  of  the  year.  It  will  be  noticed  that,  though  the  factory  had 
a  setback  due  to  delayed  material  in  the  second  week  in  October, 
it  was  able  to  exceed  the  new  schedule  during  the  early  part  of  No- 
vember and  it  made  the  three  thousand  five  hundred  cars  by  the  end 
of  the  year  as  requested. 

The  foregoing  account  will  give  a  fair  idea  of  the  application  of 
cumulative  curves  to  problems  involving  output  and  sales.  In  work 
of  this  sort,  the  cumulative  curve  is  one  of  the  most  valuable  aids 
to  the  busy  executive.  The  last  point  on  the  curve  gives  him  the 
total  output  since  the  beginning  of  the  period  for  which  the  curve 
was  plotted.  From  the  angle  of  the  curve  he  can  see  the  rate  of  output 
for  any  period  of  time  he  may  wish  to  consider.  It  must  be  kept  in 
mind  that  a  cumulative  curve  never  trends  downward.  It  can  move 
only  upward  or  horizontally.  If  there  is  no  output  during  any  period 
of  time  the  curve  simply  moves  horizontally.  Like  a  clock  recording 
time,  it  cannot  go  backward. 

Though  the  cumulative  curve  proper  cannot  go  backward,  a 
modified  curve  may  nevertheless  be  made  to  show  quantities  which 
have  been  added  to  and  subtracted  from,  giving  total  net  quantities. 
Thus  the  modified  cumulative  curve  may  be  used  to  show  the  quan- 
tities of  stock  on  hand,  additions  to  stock  being  plotted  upward  and 
reductions  to  stock  being  plotted  downward.  Any  point  on  the  curve 
then  shows  the  quantities  on  hand  at  that  particular  time.  In  mak- 
ing a  curve  like  this  it  is  ordinarily  the  practice  to  strike  a  balance 
of  the  additions  and  reductions  for  the  latest  period  of  time,  and 
then  to  change  the  curve  only  by  the  net  amount  added  or  taken  away. 
Such  a  curve  gives  not  only  a  perpetual  inventory  in  the  last  point 
plotted,  but  it  shows  the  quantity  on  hand  at  different  seasons  of  the 
year  as  a  guide  for  future  operations.  A  curve  of  this  kind  can  be 
plotted  for  the  total  number  of  men  employed  in  a  large  organization 
just  as  well  as  for  quantities  of  goods  in  store  rooms. 

Fig.  134  was  photographed  from  a  sheet  of  co-ordinate  paper 
specially  ruled  for  convenience  in  curve  plotting.     The  paper  is  eight 


CUMULATIVE    CURVES  153 

and  a  half  by  eleven  inches  (a  standard  letter-sheet  size),  and  has  co- 
ordinate ruling  printed  in  green  ink  with  wide  margins  on  all  four 
edges  to  allow  space  for  lettering,  scales,  etc.  Note  in  Fig.  134  that 
the  green  ink  of  the  co-ordinate  lines  shows  much  lighter  in  color 
than  the  black  drawing  ink  used  for  the  scales  and  the  curves.  Though 
the  co-ordinate  lines  are  distinct  enough  for  ease  in  reading  they  are 
not  nearly  so  conspicuous  as  they  would  be  if  a  line  cut  had  been  used 
instead  of  a  half-tone.  In  making  a  line  cut,  the  green  lines  of  the 
paper  must,  of  course,  be  printed  as  black  and  the  color  value  of  the 
green  lines  is  entirely  lost.  The  finished  line  cut  shows  only  the  rela- 
tive widths  of  lines,  not  relative  colors.  For  many  illustrations  of 
curves,  conspicuous  co-ordinate  lines  are  not  desired.  In  such  cases 
it  is  better  to  use  a  half-tone,  as  has  been  done  in  Fig.  134,  than  to  use 
a  line  cut. 

In  Fig.  135  we  have  curves  for  two  successive  fiscal  years  plotted 
so  that  they  may  be  compared  easily.  The  double-line  curves  and  the 
dotted-line  curves  are  plotted  to  show  the  rate  of  shipments,  while 
the  heavy-line  curves  are  plotted  on  a  cumulative  basis  and  give  the 
total  number  of  carloads  shipped  since  the  beginning  of  each  fiscal 
year.  Ordinarily  it  is  not  desirable  to  put  on  one  sheet  of  paper  curves 
giving  both  rate  of  output  and  cumulative  output,  as  there  is  danger 
of  confusing  in  the  reader's  mind  two  different  types  of  curves.  This 
illustration  is  included  simply  to  show  the  possibility  of  comparing 
two  cumulative  curves  for  succeeding  years  by  plotting  both  cumu- 
lative curves  on  the  same  sheet. 

It  must  be  remembered  that  cumulative  curves  always  refer  to 
some  definite  length  of  time  and  that  they  must  always  begin  at  the 
beginning  of  the  period  for  which  the  summation  is  made.  Cumulative 
curves  do  not  extend  outward  indefinitely,  but  start  over  again  at 
zero  with  each  succeeding  period  of  time.  Thus,  cumulative  curves 
plotted  by  months  or  weeks  on  a  long  sheet  of  paper,  for  a  series  of 
years,  would  be  seen  in  the  shape  of  saw  teeth,  with  the  highest  point 
at  the  end  of  each  fiscal  year  and  then  a  drop  to  zero  again  at  the 
beginning  of  the  next  fiscal  year.  The  saw-tooth  shape  makes  it 
feasible,  and  sometimes  desirable  for  easy  comparison,  to  plot  cumu- 
lative curves  for  several  successive  periods  of  time  in  the  same  space, 
as  the  two  cumulative  curves  in  Fig.  135  are  plotted. 

The  progressive  average  shown  by  means  of  the  dotted  lines  in  Fig. 
135  is  obtained  by  averaging  each  month  the  values  for  all  the  points 


154  GRAPHIC    METHODS 

given  on  each  curve  since  the  beginning  of  each  fiscal  year.  For  No- 
vember the  average  includes  two  months,  for  December  three  months, 
for  January  four  months,  etc.  The  progressive  averages  in  this  chart 
mean  comparatively  little  and  can  be  of  almost  no  assistance  to  the 
manager  studying  them.  The  daily  averages  and  the  progressive 
averages  would  have  been  much  more  striking  if  the  averages  for  the 
two  years  had  been  plotted  horizontally  instead  of  as  superimposed 
curves.  A  moving  average  could  then  be  shown  continuously  so  that 
the  average  would  always  take  in  twelve  months  without  having  to 
start  over  again  at  the  beginning  of  the  second  fiscal  year.  The  in- 
formation in  Fig.  135  would  have  been  more  simple  in  appearance 
and  more  quickly  apprehended  if  it  had  been  given  on  two  separate 
sheets  of  paper,  the  daily  average  curve  and  the  suggested  moving- 
average  curve  being  shown  for  two  years  horizontally  on  one  sheet,  the 
cumulative  curves  being  shown  on  a  different  sheet  with  the  two  years 
superimposed  on  the  same  scale,  as  in  Fig.  135. 

It  is  frequently  desirable  to  show  two  cumulative  curves  on  the 
same  ruled  sheet  of  co-ordinate  paper  so  that  each  curve  may  be 
studied  separately  and  the  distances  between  the  curves  noted.  Thus, 
in  Fig.  136,  the  upper  curve  shows  the  amount  of  money  loaned  since 
the  beginning  of  the  operation  of  a  factory  loan-department.  The 
lower  curve,  the  dotted  line,  indicates  the  amount  of  money  repaid 
by  the  persons  obtaining  loans  since  the  beginning  of  the  department. 
The  difference  between  these  two  curves  thus  represents  the  amount 
of  money  outstanding  at  the  end  of  any  month.  At  the  bottom  of 
the  chart  the  actual  amount  of  money  outstanding  is  plotted,  also 
in  the  form  of  a  curve.  On  the  curve  showing  the  amount  outstanding 
the  height  of  each  point  above  the  zero  line  represents  the  distance 
between  the  two  cumulative  curves  in  the  upper  portion  of  the  chart. 
It  is  much  easier  to  see  fiuctuations  if  the  amount  outstanding  is  plotted 
in  this  way  from  the  zero  line  than  if  one  must  gauge  the  amount 
outstanding  by  reading  the  space  between  two  fluctuating  cumulative 
curves.  When  data  must  be  read  by  the  length  of  vertical  lines  be- 
tween two  curves,  the  eye  is  likely  to  take  as  the  distance  between 
the  curves  the  shortest  distance  instead  of  the  distance  measured  on 
the  vertical  ruled  lines. 

In  Fig.  136  it  was  very  important  to  watch  the  total  amount  out- 
standing, for  the  fund  available  for  loans  from  the  beginning  of  the 
loan  system  until  January,  1912,  was  limited  to  $200.    From  January, 


CUMULATIVE    CURVES 


155 


Cars  Shipped 

Monthly  Daily 
2000     10 


1800  9 

1600  8 

14.00  7 

1200  6 

1000  5 

800  4 

600  3 

400  2 

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jCumulotive    Carloads 
Shipped 

Adapted  from  Factory 


Fig-  135'    Carload  Shipments  from  a  Manufacturing  Plant 

Two  separate  fiscal  years  are  compared  on  the  chart.  The  right-hand  scale  shows  monthly  averages  of  the 
number  of  carloads  shipped  per  day  of  factory  operation.  The  double-line  curves  for  daily  averages 
and  the  dotted-line  curves  for  progressive  averages  are  read  from  the  right-hand  scale.  The  heavy 
solid-line  curves  are  read  from  the  left-hand  scale  and  show  cumulatively  the  total  number  of  carloads 
shipped  since  the  beginning  of  each  fiscal  year 

1912,  until  the  end  of  the  period  under  consideration  the  fund  avail- 
able for  loans  was  $500,  of  which  $30  (reserved  for  a  special  purpose) 
could  not  be  used  for  the  loans  for  which  these  curves  were  plotted. 
Note  that  in  January,  1912,  the  amount  outstanding  exceeded  the 
funds  formerly  available  for  loans,  and  thus  required  an  increase  in 
the  capital  of  the  loan  fund.  Though  the  lettering  of  this  chart  is 
not  as  clear  as  it  should  be,  the  chart  is  nevertheless  an  excellent 
presentation  of  facts  and  a  good  demonstration  of  the  utility  of  cumu- 
lative curves. 


156 


GRAPHIC    METHODS 


Fig.  137  shows  in  detail  for  the  same  loan  department  the  opera- 
tions which  are  summarized  in  Fig.  136.  In  Fig.  137  the  heavy  line 
shows  the  actual  amount  of  money  loaned  each  month,  while  the 
dotted  line  shows  the  amount  of  money  paid  back  each  month.  The 
data  for  these  two  curves  were  later  added  month  by  month  on  a 
cumulative  basis   and  plotted  into  the  two  curves,   "Loaned"   and 


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Fig.  136.  Total  Loans  Made  to  Employees  by  a  Large  Industrial 
Corporation  and  Total  Amount  Paid  Back,  Shown  Monthly  Since 
the  Beginning  of  Loans 

The  two  upper  curves  are  plotted  on  a  cumulative  basis.  The  bottom  curve  shows  the 
amount  outstanding  and  is  equivalent  to  the  vertical  distance  between  points  on 
the  two  upper  curves.  The  capital  devoted  to  loans  is  indicated,  and  the  chart 
permits  easy  reading  of  the  amount  of  capital  not  on  loan  at  the  end  of  any  month 

**  Paid-back,"  in  Fig.  136.  Because  of  the  great  fluctuation  in  the 
amount  loaned  and  paid  back  each  month,  the  operation  of  the  depart- 
ment as  a  whole  can  be  seen  much  more  easily  from  the  cumulative 
curves  of  Fig.  136  than  from  the  actual  monthly-loan  curves  of  Fig.  137. 
In  general,  the  cumulative  curve  is  of  very  great  assistance  in  showing 
phenomena  in  which  there  are  violent  fluctuations  such  as  are  seen 
in  the  loan  curve  in  Fig.  137. 

It  is  interesting  to  note  in  Fig.  137  that  the  peaks  and  valleys 
in  the  curve  showing  the  amount  paid  back  follow  ordinarily  one  or 
two  months  behind  the  peaks  and  valleys  in  the  curve  showing  the 


CUMULATIVE    CURVES 


157 


amount  loaned.  This  is  entirely  natural,  for  these  loans  were  made 
only  in  cases  of  extreme  emergency  when  employees  were  in  tem- 
porary need.  This  relation  of  two  curves  to  each  other,  with  the  peaks 
of  one  curve  following  at  some  definite  distance  behind  the  peaks  of 
another  curve,  is  generally  referred  to  as  "lag."  Students  of  eco- 
nomics are  continually  finding  curves  which  are  seen  to  have  a  very 
great  dependence  upon  each  other  when  "lag"  is  taken  into  account. 
If  "lag"  is  not  considered,  a  great  difference  in  the  shape  of  the  curves 
might  be  taken  to  show  that  there  was  absolutely  no  relation  between 
the  facts  from  which  the  curves  were  plotted. 


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Fig.  137.  Loans  Each  Month  Made  to  Employees  of  a  Large  Indus- 
trial Corporation  and  Amounts  Paid  Back  Each  Month.  Number 
of  Accounts  Opened  and  also  Number  of  Accounts  Closed  Are 
Shown  on  a  Cumulative  Basis 

Note  how  the  curve  for  repayment  lags  behind  the  peaks  and  valleys  of  the  curve  for 
loans.  The  extent  of  the  lag  gives  a  good  idea  of  the  length  of  time  loans  are  out- 
standing.    This  illustration  is  for  the  same  loan  department  shown  in  Fig.  136 

Great  care  must  ordinarily  be  taken  in  determining  to  just  how 
great  an  extent  the  element  of  "lag"  enters  in.  The  best  way  of  de- 
termining this  is  to  plot  the  two  curves  on  separate  sheets  of  trans- 
parent bond  paper,  tracing  paper,  or  tracing  cloth,  plotting  each  curve 
to  a  separate  scale,  if  necessary,  so  that  the  peaks  and  valleys  in  the 


158  GRAPHIC    METHODS 

two  curves  will  be  as  nearly  as  possible  at  equal  distances  from  the  zero 
line.  It  is  difficult  to  prove  a  *'lag"  unless  the  scales  are  selected  so 
that  the  peaks  and  valleys  in  the  two  curves  are  at  the  same  height 
above  zero.  After  the  two  curves  have  been  plotted  separately  to 
carefully  selected  scales,  they  may  be  superimposed  and  read  through 
both  sheets  of  paper  held  in  front  of  a  bright  light.  As  the  horizon- 
tal scales  for  the  two  curves  are  the  same,  it  will  be  found,  if  the 
curves  depend  upon  each  other  without  the  element  of  "lag,"  that 
the  peaks  and  valleys  will  almost  coincide.  If  there  is  "lag,"  it  will 
be  found  necessary,  in  order  to  make  the  peaks  and  valleys  coincide, 
to  shift  one  sheet  horizontally  over  the  other  so  that  the  horizontal 
scales  disagree.  When  the  paper  has  been  shifted  back  and  forth  un- 
til the  nearest  possible  coincidence  of  the  two  curves  has  been  ob- 
tained, the  extent  of  the  "lag"  may  be  determined  by  seeing  how  far 
the  two  horizontal  scales  are  out  of  agreement.  "Lag"  is  an  impor- 
tant feature  of  many  different  sets  of  curves  and  must  be  kept  con- 
stantly in  mind  when  curves  are  being  compared. 

In  Fig.  137  the  growth  in  the  importance  of  the  loan  department 
can  readily  be  seen  by  considering  the  twelve-months  progressive 
moving  average  showing  the  average  total  monthly  loans.  Though 
there  is,  in  January,  1912,  a  very  high  peak  which  overshadows  all 
other  peaks,  the  general  tendency  of  the  curve  is  still  rapidly  upward, 
because  of  the  fact  that  a  number  of  high  points  follow  each  other 
in  close  succession,  each  nearly  as  high  as  the  peak  of  January,  1913, 
which  stands  out  alone  with  low  points  on  either  side. 

The  number  of  separate  loan  accounts  opened  and  the  number  of 
accounts  closed  is  shown  in  Fig.  137  by  means  of  cumulative  curves. 
The  fact  that  the  cumulative  curve  for  the  number  of  accounts  closed 
follows  so  nearly  the  angle  of  the  cumulative  curve  for  the  number 
of  accounts  opened,  shows  that  the  number  of  accounts  outstanding 
has  not  greatly  increased.  It  also  shows  that  since  numerous  accounts 
are  being  closed,  the  loans  are  being  made  to  other  employees  rather 
than  being  repeated  continually  to  the  same  employees. 

Fig.  138  is  a  study  made  to  determine  the  size  of  tank  necessary 
to  supply  sufficient  boiler-feed  water  for  a  number  of  locomotives 
and  tugboats.  The  average  amount  of  water  used  each  day  by  all 
the  locomotives  combined  is  given  in  the  lower  cumulative  curve. 
The  shape  of  the  curve  shows  that  locomotives  fill  their  tanks  chiefly 
between  six  and  nine  o'clock  in  the  morning  and  between  five  and 


CUMULATIVE    CURVES 


159 


titoix 


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Fig.  138.  Cumulative  Curves  Plotted  to  Determine  the  Minimum  Size  of  Tank  and 
the  Minimum  Steady  Flow  of  Water  Required  for  a  Group  of  Locomotives  and 
a  Group  of  Tugboats  Taking  Boiler-Feed  Water  from  the  Same  Source  of  Supply 

Curves  for  locomotives  and  tugs  are  plotted  separately.  A  third  curve  is  then  made  by  adding  the  vertical 
distances  of  points  on  the  two  curves  to  get  the  vertical  distance  for  points  on  the  third  curve.  The 
sloping  straight  line  shows  the  minimum  rate  of  steady  flow.  The  greatest  vertical  distance  between 
the  sloping  line  and  the  combined  curve  shows  the  necessary  minimum  tank  capacity 

seven  at  night.  The  points  are  plotted  in  the  middle  of  each  space 
because  the  values  are  based  on  the  average  quantity  of  water  taken 
between  any  two  hours  specified  in  the  horizontal  scale.  The  next 
curve  above  gives  on  a  cumulative  basis  the  average  of  the  amount 
of  water  taken  by  the  tugboats  each  da}".  It  can  be  seen  that  the 
tugs  take  water  between  six  and  eight  in  the  morning  and  between  four 
and  eight  at  night,  the  greatest  quantity  of  water  being  taken  be- 
tween seven  and  eight.  In  order  to  see  what  would  happen  if  the  loco- 
motives and  the  tugs  should  take  water  from  the  same  tanks,  the 
combined  curve  was  made  for  both  locomotives  and  tugboats  by 
adding  the  quantities  for  each  one-hour  period.  The  easiest  way  to 
make  a  combined  curve  when  only  two  curves  are  to  be  combined, 
is  to  use  a  pair  of  dividers,  taking  the  vertical  distance  above  zero 
for  each  point  on  one  curve  and  stepping  off  that  measured  distance 
above  each  point  on  the  other  curve.     The  prick  marks  showing  the 


160 


GEAPHIC    METHODS 


CUMULATIVE    CURVES  161 

distances  stepped  off  by  the  dividers  locate  the  new  combined  curve 
so  that  it  can  be  quickly  drawn  in.  The  combined  curve  in  Fig.  138 
shows  at  a  glance  that  the  locomotives  and  tugs  together  take  water 
in  such  manner  that  the  greatest  rate  of  flow  from  the  tank  occurs 
between  six  and  eight  in  the  morning. 

One  problem  involved  in  Fig.  138  was  to  determine  the  minimum 
steady  rate  of  flow  into  the  tank  and  the  size  of  the  tank  so  that  there 
would  always  be  sufficient  water  available.  By  drawing  a  line  diag- 
onally touching  the  hump  on  the  curve  between  seven  and  eight 
in  the  morning  and  the  hump  on  the  curve  between  six  and  seven 
at  night,  we  get  at  once  the  smallest  size  flow  which  will  keep  the  tank 
full  throughout  the  whole  twenty-four  hours  if  locomotives  and  tugs 
always  draw  out  the  water  as  the  average  curves  shown  in  Fig.  138 
would  indicate.  The  actual  rate  per  hour  at  which  the  water  should 
flow  is  obtained  most  easilj^  b}^  assuming  a  horizontal  distance  of 
several  hours  on  the  scale,  and  then  reading  upward  to  the  diagonal 
line  that  vertical  distance  which  corresponds  with  the  horizontal 
distance  taken.  Thus,  if  from  the  point  on  the  line  for  40,000  at  which 
the  diagonal  line  intersects  the  vertical  line  for  five  a.  m.,  we  count  10 
blocks  horizontally  to  the  right,  we  see  that  it  takes  9.1  blocks  before 
we  again  reach  the  diagonal  line.  Nine  and  one-tenth  vertical  blocks 
correspond  on  the  scale  to  45,500  gallons  of  water  flowing  in  10  hours, 
so  that  the  minimum  steady  rate  of  flow  must  be  4,550  gallons  per  hour. 

The  dimension  marks  at  "C"  and  "D"  indicate  the  great  amount 
of  water  used  between  four  and  eight  p.  m.  The  diagonal  line  drawn 
parallel  to  the  minimum-flow  line  shows  the  amount  of  water  which 
flows  into  the  tank  between  three  and  eight  p.  m.,  thus  reducing  the 
quantity  to  be  supplied  from  the  storage  space  of  the  tank  to  the 
amount  indicated  on  the  vertical  scale  by  the  dimension  mark  "C". 
Between  six  and  eight  a.  m.,  when  the  amount  which  can  flow  into 
the  tank  through  the  regular  flow-pipe  is  limited  to  the  quantity 
indicated  by  the  dimension  mark  "B",  the  draught  on  the  tank  is 
so  rapid  that  all  of  the  water  indicated  by  the  dimension  mark  "A" 
must  be  furnished  by  the  storage  capacity  of  the  tank  itself.  The 
water  does  not  flow  into  the  tank  nearly  so  fast  as  it  is  taken  out  by 
the  tugs  and  locomotives  at  that  particular  time  of  the  day.  If  we 
count  the  squares  included  vertically  in  the  dimension  line  "A"  we 
find  7.6  squares.  This  shows  that  the  amount  of  water  which  must 
be  furnished  by  the  tank  during  the  rush  hours  cannot  be  less  than 


162  GRAPHIC    METHODS 

7.6  times  5,000  (the  value  for  each  square  on  the  scale),  or  38,000 
gallons.  The  distance  "A"  is  really  the  same  as  the  vertical  distance 
between  the  point  representing  the  average  for  the  hour  from  five 
to  six  a.  m.  and  the  diagonal  line  of  minimum  flow.  The  storage 
capacity  necessary  in  any  case  of  this  sort  is  very  simply  determined 
by  means  of  curves  or  mass  diagrams  on  the  general  scheme  of  Fig. 
138.  The  measurement  of  the  greatest  distance  which  shows  between 
any  depression  in  the  consumption  curve  and  the  minimum-flow  line 
which  joins  the  peaks  on  either  side  of  it  gives  the  minimum  steady 
rate  of  flow. 

There  is  great  practical  value  in  charts  like  Fig.  138.  In  this 
case  the  minimum-flow  line  determines  the  size  of  the  pipe,  pumps, 
or  other  machinery  which  must  be  installed  to  provide  the  requisite 
quantity  of  water  if  the  water  is  kept  running  steadily  all  the  time. 
The  tank  capacity  must  be  as  great  as  the  diagram  demands  or  there 
will  not  always  be  sufficient  water.  In  practice,  it  would,  of  course, 
be  customary  to  put  in  a  pump  considerably  larger  than  that  needed 
to  provide  the  minimum  flow  which  the  chart  shows  to  be  necessary, 
and  the  tank  would  also  be  of  larger  capacity  than  the  minimum- 
storage  determination  of  the  curve  would  indicate.  The  extra  capacity 
of  both  pump  and  tank  are,  however,  only  a  safeguard  against  ab- 
normal conditions.  The  graphic  solution  shows  the  exact  rate  of  flow 
and  the  storage  capacity  which  would  be  satisfactory  if  the  conditions 
indicated  by  the  data  on  the  curves  were  to  be  constantly  maintained. 

Fig.  139  shows  the  application  of  the  cumulative  or  mass  curve 
to  problems  of  municipal  water-supply.  In  working  up  data  for 
rainfall  in  different  watersheds  and  determining  the  greatest  possible 
amount  of  water  which  can  be  obtained  from  watersheds  when  dif- 
ferent sizes  of  reservoirs  are  used,  the  cumulative  curve  is  almost 
indispensable.  In  Fig.  139  the  method  is  nearly  identical  with  that 
used  in  Fig.  138,  except  that  in  Fig.  139  we  are  determining  the  great- 
est possible  rate  of  uniform  consumption  from  a  fluctuating  supply, 
instead  of  determining  the  smallest  possible  rate  of  uniform  supply  for 
a  fluctuating  consumption.  In  Fig.  139,  the  lines  beginning  at  the 
hump  in  1870  are  drawn  at  different  angles  to  touch  the  different 
humps  and  show  various  rates  of  possible  consumption.  These  flow 
lines  are  also  continued  in  the  other  sections  of  the  curve  just  as  if 
the  curve  had  been  shown  continuously  in  one  line  instead  of  in  three- 
separate  sections.    The  scale  for  Fig.  139  is  selected  to  show  "million 


CUMULATIVE    CURVES  103 

gallons  per  square  mile."  The  scale  could  just  as  well  have  been 
made  to  show  the  total  gallons  of  rainfall  in  the  whole  watershed, 
but  it  was  more  convenient  to  put  the  scale  on  a  square-mile  basis, 
dividing  the  total  rainfall  by  the  number  of  square  miles  in  the  w^ater- 
shed. 

Cumulative  or  mass  curves  are  very  frequently  used  for  the  study 
of  quantities  in  earth  work,  especially  in  railroad  construction.  Cumu- 
lative curves  showing  the  total  quantities  of  earth  removed  from  cuts 
and  the  total  amount  used  in  fills  can  be  kept  to  give  the  whole  in- 
formation in  the  most  convenient  form  for  quick  reference  and  accurate 
study. 


Chapter  X 


FREQUENCY  CURVES.     CORRELATION 


MANY  business  problems  can  be  studied  most  rapidly  and  con- 
veniently if  the  data  are  put  in  the  form  of  frequency  curves. 
Though  engineers  have  used  curves  for  many  years  to  repre- 
sent data  relating  to  the  laws  of  physics,  the  engineer  has  made  prac- 
tically no  use  of  frequency  curves  such  as  are  used  by  the  biologist. 
This  is  probably  due  to  the  fact  that  the  engineer  can  determine  the 
laws  of  physics  from  mathematical  computations  based  on  a  relatively 
small  number  of  observations,  while  the  biologist  must  deal  with 
statistical  averages  based  upon  observations  and  measurements  in 
thousands  of  different  cases.  The  laws  of  biology  are  not  so  definitely 
mathematical  as  those  of  engineering  and  physics.  The  biologist 
must  have  more  observations  than  the  engineer  if  he  is  to  draw  accu- 
rate conclusions. 

A  frequency  chart  is  based  on  the  number  of  times  a  certain  char- 
acteristic is  found  repeated  in  a  large  number  of  observations.  The 
number  of  repetitions  is  referred  to  as  the  "frequency".    A  comparison 


C.  B.  Davenport,  in  Popular  Science  Monthly 

Fig.  140.  Frequency  Chart  Based  on  the  Number  of  Ribs  in  Scallop  Shells.  Shells 
Are  Sorted  into  Different  Piles  According  to  the  Number  of  Ribs,  the  Piles  (from 
Left  to  Right)  Having  Respectively  15,  16,  17,  18,  19  and  20  Ribs 

The  heights  of  the  different  piles  show  the  relative  frequency  of  shells  having  the  different  numbers  of  ribs. 
Seventeen-rib  shells  were  found  much  more  commonly  than  shells  with  any  other  number  of  ribs. 
a  line  were  drawn  through  the  tops  of  the  different  shell  piles,  we  should  have  a  frequency  curve 

164 


FREQUENCY   CURVES 


165 


Fig. 


relating  to  the  frequency  with  which  different  characteristics  or  items 
are  found  repeated  is  commonly  referred  to  by  the  biologist  as  "fre- 
quency distribution",  and  the  charts  showing  frequency  are  quite 
often  called  "distribution  charts"  or  "distribution  curves". 

In  Fig.  140  a  frequency  diagram  is  shown  at  the  right  by  photo- 
graphing piles  of  shells  arranged  so  that  all  shells  in  any  one  pile  con- 
tain the  same  number  of 
ribs.  The  pile  of  shells  at 
the  left,  having  the  smallest 
number  of  ribs,  contains 
but  three  shells.  In  the  pile 
of  shells  at  the  extreme 
right,  having  the  highest 
number  of  ribs,  there  is  only 
one  shell.  The  middle  pile 
shows  conclusively  that  the 
greatest  number  of  the  shells 
have  seventeen  ribs.  There 
is  a  fairly  large  number  of 
shells  in  the  pile  for  sixteen 
ribs,  and  a  somewhat  greater 
number  of  shells  in  the  pile 
for  eighteen  ribs.  Though 
it  is  unfortunate  that  no 
horizontal  scale  or  vertical 
scale  is  shown  in  the  picture, 
the  reader  will  nevertheless  be  able  to  see  from  this  illustration  the 
general  scheme  on  which  frequency  curves  are  based. 

In  Fig.  141  a  group  of  men  have  been  arranged  in  different  rows. 
There  is  only  one  man  in  the  shortest  class  at  the  left,  and  only  one 
man  in  each  of  the  tallest  two  classes  at  the  right.  Most  of  the  men 
are  of  that  height  shown  by  the  row  to  the  right  of  the  center  of  the 
diagram.  A  glance  at  the  photograph  taken  looking  down  on  this  group 
of  men  shows  that  there  are  more  men  shorter  than  the  most  fre- 
quent height  than  there  are  men  taller.  If  an  ink  line  were  drawn  as 
a  smooth  curve  to  represent  the  outline  of  the  whole  group  of  men, 
when  arranged  in  rows  as  shown  here,  the  top  of  the  curve  at  the 
end  of  the  longest  row  would  be  called  the  "mode",  as  it  would  show 
the  type  found  most  frequently  in  all  the  individuals  under  observation. 


C.  B.  Davenport,  in  Popular  Science  Monthly 

141.  Forty  University  Students  Arranged  in 
Rows,  According  to  Stature  by  Inches,  as 
follows:  56  to  57.9,  58  to  59.9,  60  to  61.9, 
62  to  63.9,  64  to  65.9,  66  to  67.9,  68  to  69.9, 
70  to  71.9 

This  illustration  gives  a  good  idea  of  the  basis  on  which  a 
frequency  chart  is  constructed.  A  rough  frequency  curve 
could  be  made  by  drawing  a  line  through  the  ends  of  all 
the  different  rows  of  men.  The  curve  would  show  a 
definite  peak  for  the  height  64  to  65.9  inches.  Such  a 
peak  is  called  the  "mode",  since  it  shows  the  type  which 
occurs  with  greatest  frequency 


166 


GRAPHIC    METHODS 


NUMBER  OF  PERSONS  WORKIN60N 

Cloak  and  Suit  Industry 

ANDAB0VETHE5 

Dress  and  Waist  1 

/       \ 

IXTH  FLOOR 

ndustry 

ll 

10 
19 
W 
17 
(6 
15 

1      1 

— 

170     20 

40     19 

47      18 

140     17 

257     16 

406     15 

62     M 

287     0 

3173     12 

4194     11 

4004^   K) 

3242      9 

3293     e 

4494      r 

5199     6 

— 

— 

47 

121 

25 
388 

91 
2347 
234« 
2584 
2823 
2353 
2583 
3416 

69.12% 
Women 

1      j 

1 

1 

i 

14 

. 

13 

, 

12  ^^^H 

1 



II 

1 

1 

9^^^M 

e^^^H 

c 

IB 

1 

5 

4 

i 
24.3t>%       , 
Women      ' 

1 

\ 

<ix)  rtoo  xbo  «)ao  idoo  Mi 

» 

wbo    UiXJ    JtiM    tiiXI    iJoo   n. 

00 

In  the  following  illustrations,  curves  of  this  kind  will  be  noticed  using 
the  diagrammatic  form  rather  than  the  actual  photographs  of  a  classi- 
fied group  like  Fig.  141.  In  Fig.  141  it  is  regrettable  that  the  illustra- 
tion does  not  show  a  scale  giving  for  each  row  the  maximum  and  mini- 
mum height  of  men  in  that  row.  Some  scheme,  of  course,  was  neces- 
sary to  divide  these  men  up  into 
height  classes,  but  the  reader  has 
no  way  of  knowing  the  limits  of 
height  for  each  class  except  by  re- 
ferring to  the  title  of  the  illustra- 
tion. 

Frequency  charts  are  some- 
times made  for  popular  illustra- 
tion by  drawing  vertical  lines  to 
represent  the  number  of  individ- 
uals found  in  each  class  designated 
by  the  horizontal  scale.  Thus,  a 
representation  could  be  made  for 
the  data  of  Fig.  141  by  having  a 
horizontal  scale  to  represent 
heights,  and  drawing  vertical  lines 
to  a  scale  by  which  the  length  of 
each  vertical  line  or  bar  would 
represent  the  number  of  individ- 
uals of  that  particular  height.  The 
series  of  bars  would  then  have  the 
same  general  arrangement  as  the 
photograph  of  Fig.  141  representing  the  number  of  men  actually  seen. 
These  bar  diagrams  to  represent  frequency  are  not  of  very  great  use, 
except  possibly  in  advertising  w^ork  where  it  may  be  necessary  to  get 
some  kind  of  chart  which  can  be  understood  by  any  untrained  reader. 
In  Fig.  142  an  effective  use  has  been  made  of  the  frequency-curve 
scheme  in  a  report  intended  for  wide  circulation  among  persons  who 
have  not  been  trained  in  reading  curves.  The  general  outhne  of  a 
tall  New  York  manufacturing  building  is  given  very  clearly  as  a  field 
of  co-ordinate  ruling,  on  which  the  actual  numbers  of  workers  for  any 
floor  level  can  be  read  from  the  horizontal  scale  with  a  fair  degree; 
of  accuracy.  The  numbers  working  below  the  sixth  floor  are  very 
large,    and    only    those    on    and    above   the    sixth    floor    are    shown. 


Joint  Jiuard  of  Sanilary  Control,  New  York  CitJj 

Fig.  142.  The  Number  of  Persons  Work- 
ing On  and  Above  the  Sixth  Floor 
in  the  Cloak  and  Suit  Industry  and 
the  Dress  and  Waist  Industry  in 
New  York  City 

This  chart  was  made  first  for  a  wall  exhibit  and  was 
later  used  in  a  widely  distributed  report.  The 
co-ordinate  ruling  has  the  shape  of  a  New  York 
manufacturing  building.  By  observing  this  illus- 
tration from  the  left  edge  of  the  page  the  reader 
may  get  the  general  effect  of  a  frequency  curve 


FREQUENCY   CURVES 


167 


This  allows  the  use  of  a  large  scale  for  the  data  of  the  upper  floors. 
In  order  to  see  the  general  shape  of  a  frequency  curve  when  plotted 
with  flat  tops  instead  of  peaked  tops,  the  book  may  be  turned  so 
that  the  illustration  is  seen  from  the  left-hand  edge.  This  chart  was 
drawn  primarily  as  a  wall  exhibit,  to  be  used  later  as  an  illustration 
in  a  printed  report.  The  general  scheme  is  excellent  and  it  could 
scarcely  be  improved  upon,  even  though  the  independent  variable 
has  here  been  made  the  vertical  scale  instead  of  the  horizontal  scale. 
Putting  these  data  in  the  form  of  a  curve  such  as  is  used  in  Fig.  143 
would  probably  not  be  as  effective  for  untrained  readers  as  the  black 


bars  of  Fig.  142, 
placed  against  a  field 
in  the  general  shape 
of  a  New  York  man- 
ufacturing building. 
Fig.  143  shows  a 
frequency  diagram  of 
the  kind  found  most 
useful  in  ordinary 
work.  The  vertical 
scale  here  represents 
percentage,  and  the 
total  of  all  the  figures 
shown  at  the  upper 
part  of  the  chart 
added  together  is  100 
per  cent.  Frequency 
curves  are  very  often 
used,  however,  with 
numbers  rather  than 
percentages  repre- 
sented on  the  vertical 


Tin 


N<0U>lflN-^OMN«0OO—  -NN 


22      24     26 


38      40     42      44 


28     30     32      34     36 

Aqe  at  Marriage 

Data  of  Amy  Hcwes,  in  Publications  Am.  Statistical  Assn. 

Fig.  143.  Age  at  Marriage  of  439  Married  Graduates  of 
Mount  Holyoke  College  who  Graduated  from  1890 
to  1909 

The  vertical  scale  shows  the  percentage  of  the  whole  439  who  married 
at  each  age  given  on  the  horizontal  scale.  The  totals  of  all  percent- 
age figures  at  the  upper  margin  of  the  chart  is  100  per  cent.  If  a 
greater  number  of  persons  were  included  in  a  frequency  curve  of  this 
sort  the  curve  would  be  less  irregular  and  the  mode  would  show  more 
distinctly 


scale,  and  the  vertical  scale  then  shows  the  actual  number  in  each  class. 
To  assist  the  reader,  the  total  number  of  observations  made  would 
usually  be  recorded,  perhaps  in  the  title  of  the  illustration.  In  bio- 
logical work  observations  are  usually  made  in  vast  number,  to  permit 
making  a  very  accurate  conclusion  regarding  the  general  laws  of  fre- 
quency for  any  particular  subject  under  consideration.  For  a  great 
many  problems  of  everyday  life,  however,  the  observations  are  not 


168 


GRAPHIC    METHODS 


of  sufficient  number  to  permit  the  formation  of  any  general  laws. 
Thus  for  Fig.  143  we  are  not  justified  in  saying  that  all  college  women 
marry  at  the  particular  ages  indicated  by  this  chart.  The  number 
of  women  taken  into  consideration  for  the  preparation  of  the  chart 
was  not  sufiicient  to  allow  any  final  conclusion,  certainly  not  to  justify 
any  general  statement  that  college  women  are  less  likely  to  marry  at 
the  age  of  twenty-six  than  at  either  twenty -five  or  twenty-seven. 

Aggregate  Population 
Males  Females 


o        20 

Per  Cent. 


Chinese    and  Japanese 
Males  Females 


6S  + 
55-64 

45-54. 
35-44. 
30-34 

25-29 


20-24    ^f 
15-19    ^ 
0-15 


too 


o  20 

Per  Cent 


CZI  single 


^S  Married 


Widowed 

United  Stales  Statistical  Atlas,  1900  Census 


Fig.  144.     Conjugal  Condition  of  the  Population  of  the  United  States  in  1900  in 
Proportions  of  the  Total  Number  of  Each  Age  Group 

This  chart  was  printed  in  color  in  the  Statistical  Atlas.  Here  shading  is  used  instead  of  color.  The  arrange- 
ment to  the  right  and  left  of  a  zero  line  at  the  center  makes  visual  comparison  difficult  between  the  data 
for  males  and  females.  Note  the  contrasts  between  the  upper  and  lower  charts.  Compare  the  upper 
chart  with  Fig.  145 

In  biological  work  the  number  of  observations  taken  is  ordinarily 
sufficient  to  permit  drawing  a  smooth  curve  to  represent  the  general 
law,  after  a  chart  drawn  with  numerous  straight  lines  has  been  made 
by  the  method  used  in  Fig.  143.  It  would  not  be  desirable  to  draw 
a  smooth  curve  in  the  case  of  Fig.  143,  as  the  smooth  curve  would 
be  misleading  because  of  the  small  number  of  observations  made. 
For  most  business  problems,  and  in  many  problems  actually  in  the 
field  of  statistics,  the  laws  which  affect  frequency  are  so  indefinite 


FREQUENCY    CURVES 


169 


and  the  number  of  observations  so  limited  that  it  is  much  better  to 
use  the  straight-Hne  method  of  Fig.  143  than  to  attempt  to  make  a 
smooth  curve.  Sometimes  a  smooth  curve  may  only  mislead  the 
reader,  making  the  chart  appear  very  accurate  when  in  reality  the 
data  were  so  crude  that  only  the  roughest  approximation  is  possible. 
Fig.  144  is  copied  from  the  Census  Atlas  for  the  1900  Census.  In 
the  Atlas,  colors  were  used  for  the  different  areas  which  must  be  repre- 
sented here  by  cross-hatching.  Though  these  illustrations  hold  some 
very  valuable  and  interesting  information,  the  information  is  contained 

PerCenT 
lOO 

90 

80 

70 

60 

50 

40 

30 

20 

lO 


V 

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M 

ARRIED 

\^ 

* 

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'^---. 

-^^^.. 

""     ^-...^^^^^ 

\ 

\/ 

/ 

^S'e, 

V 

A 

/ 

i 

\  h 

\ 

.^^ 

I 
1 

A 
/  \ 

\ 

S/ 

.f.^^ 

y 

1 

1     A 

#  \ 

s 

• 

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!/ 

^> 

^^G-Le^ 

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^^■^ 

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=.=:; 

ir: 

.^^^■^^ 

*""""™ 

1 

under 

15 


15-19  25-29 

20-24        30-34 


Male 


35-44        45-54         55-64 


—  --Female 


over 

65 


Fig.  145.     Conjugal  Condition  of  the  Population  of  the  United  States  in  1900  in 
Proportions  of  the  Total  Number  of  Each  Age  Group 

Here  the  arrangement  of  Fig.  144  has  been  reversed  so  as  to  place  age  on  the  horizontal  scale,  since  age 
is  the  independent  variable.  Having  the  data  expressed  in  curves  permits  much  clearer  interpretation 
by  the  reader.  Curves  for  male  and  for  female  may  be  instantly  compared.  The  term  "widowed" 
as  appUed  to  men  was  used  to  harmonize  with  the  preceding  illustration 

in  such  manner  that  it  is  almost  impossible  for  the  reader  to  get  it  out. 
In  the  first  place,  age  is  the  independent  variable,  but  it  has  been  made 
the  vertical  scale.  The  information  sought  is  the  percentage  at  different 
ages  for  each  of  the  sexes,  and  this  must  be  read  from  the  horizontal 
scale,  in  violation  of  one  of  the  most  important  rules  for  graphic  work. 
Another  bad  feature  of  the  chart  is  that  data  for  male  and  female  are 
shown  in  the  right  and  left  direction  from  the  center  line,  making  it 
almost  impossible  for  the  reader  to  compare  the  figures  for  male  and 
female  at  any  age  under  consideration.  The  data  for  the  upper  half 
of  Fig.  144  are  replotted  in  Fig.  145,  and  the  reader  would  do  well  to 


170  GRAPHIC    METHODS 

compare  the  two  illustrations  to  see  just  how  much  more  clear  Fig.  145 
is  than  Fig.  144. 

The  bottom  portion  of  Fig.  144  is  shown  here  by  way  of  contrast  with 
the  upper  portion.  Notice,  for  instance,  'the  difference  in  the  shape  of 
the  chart  for  the  female  Chinese  and  Japanese  population  of  the  United 
States  as  compared  with  the  chart  for  females  in  the  aggregate  popula- 
tion of  the  United  States.  A  very  large  percentage  of  female  Japanese 
and  Chinese  are  married  by  the  age  of  thirty-five,  but  after  that  age 
there  is  a  fairly  large  percentage  reported  as  single.  It  would  appear 
that  many  widows  must  be  reporting  themselves  as  single  instead  of 
as  widows,  or  the  chart  would  probably  not  be  so  different  in  shape  from 
the  chart  for  the  aggregate  population  of  the  United  States. 

In  Fig.  145  the  scale  for  age  has  been  properly  placed  horizontally 
and  the  scale  for  percentage  placed  vertically.  The  whole  population 
is  considered  as  single  under  the  age  of  fifteen.  The  total  of  the  figures 
for  single,  married,  and  widowed  on  any  vertical  line  equals  100  per 
cent;  thus,  as  the  number  married  in  succeeding  years  increases,  the 
number  who  are  single  is  seen  to  decrease.  The  curves  prove  at  a 
glance  that  the  women  start  to  marry  much  earlier  than  the  men. 
Between  twenty  and  thirty-five  the  horizontal  difference  between  the 
two  curves  shows  that  the  women  marry  about  four  years  earlier  than 
the  men,  or,  in  other  words,  taking  the  population  as  a  whole,  the 
women  marry  men  about  four  years  their  seniors.  In  considering 
these  curves  it  must  be  remembered  that  this  chart  is  made  up  on  a 
different  basis  from  Fig.  143.  In  Fig.  143  all  the  women  who  married  are 
recorded  as  married,  and  the  top  of  the  curve  (the  mode)  shows  at 
once  the  age  at  which  marriages  are  most  frequent.  In  this  chart,  how- 
ever, we  are  considering  three  things,  and  the  chart  shows  the  percentage 
who  recorded  themselves  as  married,  rather  than  the  actual  age  at  which 
marriage  occurred.  The  percentage  of  those  who  report  themselves 
married  is  affected  by  the  number  who  are  single  and  also  by  the  num- 
ber who  are  widowed.  If  in  the  later  age  classes,  deaths  of  husbands 
occur  more  rapidly  than  marriages  of  spinsters  for  any  particular  age, 
the  "married"  curve  will  trend  downward  even  though  a  very  large 
number  of  spinsters  may  be  marrying  at  that  age.  It  is  simply  a  ques- 
tion of  balancing  the  death  rate  of  husbands  against  the  marriage  rate 
of  spinsters.  The  curve  marked  "married"  on  this  chart  does  not  show 
the  age  at  marriage,  but  simply  shows  the  percentage  in  any  age  class 
who  report  themselves  as  married  and  not  widowed. 


FREQUENCY  CURVES  171 

The  men  marry  later  than  the  women.  Many  of  the  men  marrying 
over  forty  marrj^  women  much  younger  than  themselves.  As  the  hus- 
bands are  older  than  the  wives,  the  expectation  of  life  for  the  husband  is, 
of  course,  less  than  for  the  wives,  and  the  number  of  widows  at  any  age 
is  far  in  excess  of  the  number  of  widowers,  on  this  account  alone.  In- 
dustrial accidents,  war,  etc.,  also  tend  to  make  a  high  death  rate  among 
the  men  and  cause  more  widows  than  widowers.  In  Fig.  145  the  curve 
for  men  has  been  labeled  "widowed"  to  follow  the  Census  Office  prac- 
tice in  Fig.  144. 

With  Fig.  144  some  of  the  age  classes  are  for  an  interval  of  only  five 
.years  while  other  age  classes  have  an  interval  of  ten  years,  yet  the 
different  lengths  of  interval  are  shown  by  the  same  distance  on  the  scale. 
For  Fig.  145  the  horizontal  scale  has  purposely  been  made  such  that 
the  ten-year  age  intervals  are  set  off  by  twice  the  distance  used  for  the 
five-year  intervals.  As  there  are  very  few  marriages  under  fifteen, 
the  space  for  "under  fifteen"  has  been  made  three  times  the  space  for 
the  five-year  interval.  Taking  the  standard  life  as  four-score  years, 
the  space  for  "over  sixty -five"  has  been  made  three  times  the  distance 
used  for  the  five-year  intervals.  This  selection  of  horizontal  distances 
makes  the  curves  into  much  more  nearly  their  correct  shape  than  is 
possible  on  the  Census  Office  chart,  where  five-year  and  ten-year 
class  intervals  are  shown  by  equal  scale  distances. 

Perhaps  the  greatest  gain  made  in  clearness  in  Fig.  145  is  due  to 
the  placing  of  the  curves  for  male  and  female  on  the  same  ruled  field, 
so  that  they  can  be  compared  instantly  and  correctly  without  need 
for  any  right-hand  and  left-hand  measurements  such  as  were  necessary 
in  Fig,  144.  No  claim  is  made  that  Fig.  145  is  suitable  for  untrained 
readers.  Since,  however,  it  is  doubtful  whether  many  unskilled  read- 
ers ever  refer  to  the  Census  Atlas,  it  would  seem  desirable  to  use  the 
general  scheme  of  Fig.  145  for  clearness  and  convenience. 

In  Fig.  146,  also  taken  from  the  Census  Atlas  for  the  1900  Census, 
a  right-and-left  measurement  must  be  made  to  compare  death  rates 
in  two  different  years,  ten  years  apart.  The  chart  was  drawn  to  bring 
out  the  data  clearly  and,  if  clearness  is  not  attained,  the  data  might 
just  as  well  be  expressed  in  columns  of  figures.  Here  again  the  vari- 
ables have  been  reversed  and  the  independent  variable  improperly 
made  the  vertical  scale. 

In  Fig.  147  the  data  of  Fig.  146  are  redrawn  into  two  curves  by 
which  the  number  of  deaths  occurring  at  different  ages  can  be  readily 


172 


GRAPHIC    METHODS 


Age 

1900 

1890 

180       160       l'»0       120       100      60        60        40        20 

20      40      60      ao     100    120    140    ISO    too 

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United  States  Statistical  Atlas,  1900  Census 


Fig.  146.  Comparative  Proportion  of  Deaths  at  Different  Ages  from  Pneumonia 
per  1,000  Deaths  from  Pneumonia  in  the  Registration  Area  of  the  United  States, 
1890  and  1900 

The  right-and-left  arrangement  of  this  chart  makes  comparison  for  the  two  different  years  almost  impossible. 

Contrast  this  illustration  with  Fig.  147 

compared  for  the  two  years  under  consideration.  Notice  that  in  the 
later  year,  1900,  deaths  from  pneumonia  between  the  ages  of  ten  and 
sixty  years  were  much  less  frequent,  while  deaths  after  the  age  of 
sixty  were  more  frequent.  There  was  also  an  increase  in  the  number 
of  deaths  at  ages  less  than  four.  Certainly  the  facts  relating  to  deaths 
from  pneumonia  for  the  two  years  are  much  more  clearly  brought 
out  in  Fig.  147  than  in  Fig.  146. 

There  are  some  peculiarities  in  Fig.  147  which  should  be  pointed 
out.  The  Government  figures  are  given  by  one-year  intervals  up  to 
the  age  of  five,  and  then  on  five-year  intervals  to  ninety -five.  Fig.  147 
really  should  have  been  made  so  as  to  indicate  a  change  in  the  hori- 
zontal scale  at  five  years.  If  the  chart  had  been  made  the  full  width 
of  the  page  it  world  have  been  possible  to  get  room  enough  to  show 
the  figures  for  single  years  at  ages  under  five  by  using  a  space 
only  one-fifth  of  the  horizontal  distance  used  for  the  five-year  inter- 
vals. The  large  number  of  deaths  at  ages  five  to  nine  inclusive  is 
very  striking  on  the  curve.  Possibly  the  large  death  rate  from  five 
to  nine  may  be  due  to  the  lessening  of  parental  care  at  an  age  when 
exposure  becomes  more  frequent.  By  ten  years  of  age,  the  children 
have  learned  better  how  to  take  care  of  themselves  and  the  number 
of  deaths  from  pneumonia  comes  down  to  about  the  lowest  point. 
Though  the  foregoing  explanation  of  the  large  number  of  deaths 
from  five  to  nine  years  may  be  correct,  it  is  probable  that  the  figures 
are  more  or  less  in  error,  due  to  the  tendency  to  state  ages  in  numbers 


FREQUENCY   CURVES 


173 


perlooo 
20  O 


which  are  multiples  of  five.    The  peaks  for  the  period  five  to  nine 
may  be  due  largely  to  parents  giving  the  age  roughly  as  "five  years". 

In  Fig.  148  the  data  in  which  the  reader  is  interested  are  shown 
at  the  peaks  of  various  triangles.  The  shaded  triangles  on  the  chart 
give  a  geometrical  figure  which  at  first  glance  might  be  considered 
as  a  curve.  It  is  not  until  after  a  considerable  amount  of  puzzling 
that  one  notices  that  the  triangles  have  absolutely  no  significance 
and  that  they  are  only  a  means  of  showing  the  distance  from  the 
base  line  to  the  various  points  representing  decrease  or  increase.  It 
would  have  been  better  if  plain  black  bars  had  been  used  for  Fig.  148 
instead  of  the  tri- 
angles. Bars  are  so 
familiar  to  everyone 
that  there  would  be 
no  danger  of  error  in 
interpretation.  This 
illustration  was  used 
in  a  Sunday  new^s- 
paper  article  where 
a  non-technical  class 
of  readers  had  to  be 
reached.  For  such  a 
class  of  readers  the 
solid  black  bars 
would  probably  be 
the  most  easily  un- 
derstood method  of 
presentation. 

For  anything  ex- 
cept newspaper  pres- 
entation, the  method 
of  Fig.  149  would 
probably  be  more 
acceptable  to  the 
reader  than  the  solid 


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h'l     I     I     I     I     I     I     I     I    + 

inbinoinoinOinoin 


Fig.  147.  Comparative  Proportion  of  Deaths  at  Different 
Ages  from  Pneumonia  per  1,000  Deaths  from  Pneu- 
monia in  the  Registration  Area  of  the  United  States, 
1890  and  1900 

Comparison  of  the  two  years  can  be  made  instantly  throughout  the  whole 
range  of  ages.  Age  is  the  independent  variable  and,  hence,  is  shown 
here  as  the  horizontal  scale.  It  would  be  better  if  a  vertical  wavy 
line  or  some  other  signal  were  used  to  show  the  change  in  the  horizon- 
tal scale  for  ages  below  five  years 

black  bars  suggested  in  the  preceding  paragraph.  The  curve  drawn 
in  Fig.  149  shows  a  fairly  uniform  increase  in  death  rates  as  ages 
increase  up  to  the  age  of  sixty.  The  degree  of  uniformity  in  increase 
is  much  more  readily  seen  from  the  curve  line  than  it  could  be  shown 


174 


GRAPHIC    METHODS 


by  the  use  of  bars.  Granted  that  the  curve  of  Fig.  149  might  not 
be  understood  by  all  the  readers  of  a  newspaper,  it  is  nevertheless 
much  more  desirable,  even  in  newspaper  work,  than  the  method  shown 
in  Fig.  148.  Though  Fig.  149  might  not  attract  deep  interest  on  the 
part  of  a  newspaper  reader,  it  would  not  be  likely  to  be  misinter- 
preted. Fig.  148  might  serve  to  attract  attention,  but  what  is  the  use 
in  attracting  atten- 
tion unless  a  correct 
impression  is  given 
after  attention  has 
been  attracted  .^^ 

Frequency  curves 
thus  far  considered 
have  permitted  read- 
ing from  the  vertical 
scale  only  the  actual 
number  or  percent- 
age observed  corre- 
sponding to  any 
point  which  may  be 
selected  on  the  hori- 
zontal scale.  Thus, 
in  Fig.  143  (see  page 
167)  we  can  read 
from  the  vertical 
scale   only   the   per- 


Equllable  Life  Assurance  Society 

Fig.  148.     Change   Since  1880   in  the   Death  Rates  of 
Americans  at  Various  Ages 

The  use  of  the  separate  triangles  here  is  confusing  to  the  reader.  One  is 
apt  to  interpret  the  chart  by  the  contour  of  the  shaded  areas  rather 
than  by  the  points  at  the  tips  of  separate  triangles.  Compare  this 
illustration  with  Fig.  149 


centage  of  marriages  which  corresponds  to  any  selected  age  on  the  hori- 
zontal scale.  In  Fig.  150,  however,  we  have  the  same  data  of  Fig.  143 
plotted  in  the  form  of  a  cumulative  frequency  curve.  With  a  cumulative 
frequency  curve  the  vertical  scale  shows  not  the  actual  number  for 
any  point  of  the  horizontal  scale,  but  the  number  cumulatively  up 
to  any  point  which  may  be  selected  on  the  horizontal  scale.  In  Fig. 
143  the  percentage  who  married  at  each  age  is  given  in  figures  at  the 
top  of  the  chart.  By  observing  the  figures  at  the  top  of  Fig.  143 
and  the  figures  at  the  top  of  Fig.  150,  the  method  for  plotting  a  cumu- 
lative frequency  curve  will  be  apparent.  Beginning  with  the  per- 
centages for  the  later  ages  in  Fig.  143,  the  figures  for  the  various 
years  are  added  cumulatively  to  give  the  figures  seen  at  the  top  of 
Fig.  150.     The  figures  and  the  curve  of  Fig.  150  thus  show  the  per- 


FREQUENCY   CURVES 


175 


Q 

Q 

O 

oV 

.\* 

.\° 

<n 

oo 

m 

B 


centage  who  married  at  ages  greater  than  any  specific  age  selected 
from  the  horizontal  scale  of  the  chart. 

Fig.  151  gives  an  example  of  a  class  of  information  which  can  be 
sho\\'n  to  very  great  advantage  by  the  use  of  cumulative  frequency 
curves.  In  an  annual  report  of  a  railroad  a  tabulated  statement  of  the 
number  of  miles  of  different  weights  of  rail  in  use  at  the  end  of  the 
fiscal  year  makes  the  information  difficult  for  the  stockholder  to  inter- 
pret. Putting  the  data  in  the  form  of  a  curve  like  Fig.  151  lets  the 
stockholder  see  at  once  just  what  conditions  are  on  his  road,  in  so  far  as 
rail  weight  is  concerned.  Thus,  in  Fig.  151,  the  stockholder  may  see 
at  a  glance  that  a  very  small  percentage  of  the  rails  on  this  railroad 
weigh  in  excess  of  75  pounds  per  yard,  and  that  only  about  half  of  the 
rails  weigh  more  than  70  pounds  per  yard.  In  order  to  compare  differ- 
ent years  it  would  be  well  to  have  a  chart  of  this  kind  printed  in  the 

annual  report,  with 
curves  for  different 
years  plotted  on  the 
same  co-ordinate  rul- 
ing, so  that  the 
stockholder  could  see 
by  the  change  in  the 
shape  of  the  curves 
just  what  has  been 
done  toward  replac- 
ing light  rails  with 
heavy  rails.  If  de- 
sired, rail- weight 
curves  for  different 
railroad  systems 
could  be  shown  in 
the  same  chart,  so 
that  the  stockholder 
might  see  how  his 
railroad  compares 
with  others  in  the 
matter  of  rail  weights. 


0 

i-  o 

<u 

a 


"Qeo 


<oo 
<  ^ 


/ 

** i*-. 

/ 

/ 

' 

/ 

r 

/ 

/ 

^ 

/ 

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^^^ 

^ 

^^"^ 

SP 

Fig.  149. 


Data  of  Elmer  Rittenhouse,  of  the  Equitable  Life  Assurance  Society 

Change    Since    1880    in   the    Death   Rate    of 
Americans  at  Various  Ages 

The  increase  in  death  rates  for  ages  over  forty  is  here  shown  in  great 
contrast  with  the  decrease  in  death  rates  for  ages  less  than  forty. 
The  heavy  zero  line  and  the  arrows  pointing  upward  and  downward 
make  misinterpretation  almost  impossible 

It  would  have  been  better  if  Fig.  151  had,  at  the  lower  left-hand 
corner,  the  words  "more  than",  with  an  arrow  pointing  horizontally 
to  the  right  as  can  be  seen  in  Fig.  158.     In  cumulative  frequency  curves 


176 


GRAPHIC    METHODS 


such  as  this  it  is  well  to  give  the  reader  a  clew  that  it  is  a  cumulative 
frequency  curve  he  is  observing,  and  the  arrow  with  the  words  "more 
than"  accomplishes  this  result  in  a  satisfactory  manner. 

There  are  two  scales  used  in  Fig.  151  with  the  expectation  that  the 
reader  would  ordinarily  use  the  left-hand  scale  when  reading  the  chart, 
^oincoq  ^oot-K,  w -.<n  -  - -o<nr:  using    the    words 

ov^      off)(r)(n<nr^vfl">:K»oj-  morc  tuan    .      1  ne 

right-hand  scale 
reading  downward 
permits  the  reader  to 
get  at  once  the  com- 
plement of  any  figure 
on  the  left-hand 
scale,  so  that,  by 
using  the  right-hand 
scale,  the  reader  may 
interpret  the  curves 
on  a  "less  than" 
basis.  Thus,  in  con- 
sidering the  weight, 
roughly  6  per  cent  of 
all  the  rails  on  the 
system  are  more 
than  75  pounds  per 
yard,  and  using  the 
right-hand  scale  it  is 
seen  that,  roughly, 
75  pounds  per  yard.     There 


OVER- 


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70 

V 

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> 

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20  22   24  26  28 


34  36  38  40  42  44 


90  32 

Age 

Data  of  Amy  Hemes  in  Publications  Am.  Statistical  Assn. 


Fig.  150.  Percentage  of  439  Married  Graduates  of 
Mount  Holyoke  College  (Women)  Graduating  1890 
to  1909,  who  Married  at  Ages  Greater  than  Any 
Specific  Age  Selected  from  the  Horizontal  Scale  of 
the  Chart 

This  is  a  cumulative  frequency  curve  plotted  from  exactly  the  same  data 
as  Fig.  143.  The  word  "over"  with  the  arrow  at  the  lower  left-hand 
corner  of  the  chart  shows  that  the  chart  does  not  indicate  the  per- 
centage who  marry  at  any  age  but  the  number  who  marry  later 
than  any  specific  age  read  from  the  horizontal  scale 


94  per  cent  of  all  the  rails  are  "less  than 
is  not  ordinarily  any  necessity  for  using  a  double  scale  in  this  manner. 
It  is  done  here  only  to  show  the  difference  in  reading  a  two-scale  chart. 
In  Fig.  152  and  also  in  Fig.  153  the  cumulative  curves  have  been 
plotted  on  a  different  basis  from  that  used  in  plotting  Fig.  150  and  Fig. 
151.  In  Fig.  150  and  Fig.  151,  the  curves  begin  at  the  100  per  cent  line 
at  the  top  of  the  chart  and  extend  downward  toward  the  right.  In  Fig. 
152  and  Fig.  153  the  curves  start  at  the  zero  line  at  the  bottom  and  ex- 
tend upwards  toward  the  right  of  the  chart.  The  differences  in  the 
shape  of  the  curves  will  point  out  to  a  trained  reader  the  manner  in 
which  he  must  read  the  curves.  Fig.  152  and  Fig.  153  should  be  read 
using  the  words  "less  than"  instead  of  the  words  "more  than".     Thus, 


FREQUENCY   CURVES 


177 


Per  Cent 
A      B 


90 


in  Fig.  152  considering  the  curve  "A",  60  per  cent  of  all  the  telephone 
calls  of  this  class  were  answered  in  "less  than"  four  seconds  and  76  per 
cent  of  the  calls  were  answered  in  "less  than"  five  seconds.  Of  course, 
all  those  calls  which  were  observed  as  having  been  answered  in  "less 
than"  four  seconds  are  also  answered  in  "less  than"  five  seconds,  so 
that  the  curve  is  on  a  strictly  cumulative  basis.  In  Curve  "C"  it 
can  be  seen  that  only  30  per  cent  of  the  calls  of  that  class  were  answered 
in  less  than  four  seconds,  as  against  60  per  cent  for  curve  "A".  Though 
curve  "A"  is  higher  up  on  the  chart  than  curve  "C  ",  it  really  represents 
a  smaller  length  of  time  required  to  answer  telephone  calls  than  shown 
by  curve  "C".  Since  twice  as  large  a  percentage  of  the  calls  were 
answered  in  "less  than"  four  seconds,  the  average  time  for  answering 
calls  in  curve  "A"  is  certainly  smaller  than  the  average  time  for  curve 
"C",  yet  curve  "A"  ap- 
pears on  the  upper  part  of 
the  chart.  It  is  confusing 
to  the  average  reader  to 
have  curves  appear  on  the 
upper  part  of  a  chart  when 
they  really  represent  numer- 
ically smaller  quantities 
than  other  curves  appearing 
on  the  lower  portion  of  a 
chart.  Yet  this  is  the  result 
when  curves  are  plotted  on 
a  "less  than"  basis.  In 
order  to  avoid  danger  of 
misinterpretation,  it  seems 
desirable  that  cumulative 
frequency  curves  should  be 
plotted  on  a  "niore  than" 
basis.  Most  of  the  cumula- 
tive   frequency    curves    in 


60 


30 


20 


ID 


0 

10 
20 
30 
40 
50 
60 
70 
80 
90 
on 

"^ 

te 

\ 

\ 

\ 

^^^ 

\ 

> 

\ 

\ 

\ 

\ 

] 

X 

110 


120 


50  60  70  80  90  lOi 

Weight  of  Rail  in  Pounds 

Fig.  151.  Weight  of  Rails  per  Yard  in  the  Main 
Line  Track  of  the  Seaboard  Air  Line  Railway 
as  Published  in  the  Annual  Report  to  Stock- 
holders for  the  Fiscal  Year  Ending  June  30, 
1912 

When  using  the  left-hand  scale  the  chart  is  read  on  a  "more 
than"  basis  as  if  the  words  "more  than"  had  been  used 
with  the  horizontal  scale  as  seen  in  Fig.  158.  If  the  right- 
hand  scale  is  selected  the  words  "less  than"  are  used 


this  book  are  plotted  on  a 
"more  than"  basis,  so  that  curves  involving  the  larger  quantities  or 
percentages  may  appear  on  the  chart  above  those  cumulative  fre- 
quency curves  for  smaller  quantities  or  percentages. 

Fig.  152  and  Fig.  153  show  the  application  of  the  cumulative  fre- 
quency curve  to  commercial  problems.     The  full  explanation  of  these 


i 


178 


GRAPHIC    METHODS 


two  charts  cannot  be  gone  into  here,  but  the  reader  can  see  for  himself 
the  use  of  the  cumulative  frequency  curve  in  studying  different  problems 
in  the  telephone  business.  In  Fig.  152  the  curves  show  the  time  required 
to  answer  calls  in  different  cities,  while  Fig.  153  shows  a  comparison 
of  answering  times  in  different  classes  of  service.  Notice  that  in  each 
of  these  two  charts  it  seems  that  two  seconds  is  about  the  minimum 
which  can  be  expected  in  answering  telephone  calls  with  the  existing 
types  of  equipment.  Fig.  153  certainly  gives  in  excellent  manner  the 
comparison  between  the  answering  times  for  different  classes  of  service. 
It  would  be  very  difficult  to  convey  the  complex  information  contained 

in  Fig.  153  by  using  tabu- 


lated figures  only.  Tabu- 
lated figures  would  take  up 
as  much  space  as  the  chart 
and  they  would  be  less  in- 
telligible to  any  person  who 
knows  even  the  rudiments 
of  reading  graphic  presenta- 
tions. 

In  Fig.  154  an  attempt 
was  made  to  apply  cumu- 
lative frequency  curves  to 
a  comparison  of  wage  rates 
in  different  sections  of  th( 
United  States.    The  chart,' 
however,  is  likely  to  be  very 
misleading,  as  it  has  been 
plotted  by  methods  whici 
are  not  in  accordance  witl 


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Telephone  Service  in  Wisconsin 
Promptness  of  Operators  in  Answering  Calls          — 
Curves  Showing  Conditions  inCities  of  Various  5ize5 
A  Average  5peed  in  all  Cities  over  10,000  (nns  Calls  - 
fl         -             -      .     -    ■  of  WOO  to  10.000     634     " 
C         •             ....            Under  iOOO{  £76      ' 

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0     1      £     J    4     5     6     7     e     9     10    II     l£    13    14    15    16    n    10    19    £0 
Time  of  Answer  in  5econcb 

Courtesy  of  Data,  Chicago 

Fig.  152.  Time  Required  for  Operators  to  An- 
swer Telephone  Calls  in  Towns  of  Different 
Size  in  Wisconsin 

These  curves  start  at  the  lower  left-hand  portion  of  the  field 
and  trend  upward,  showing  that  they  are  plotted  on  a 
"less  than"  basis.  Curve  A  shows  a  smaller  time  required 
to  answer  calls  than  Curves  B  or  C,  yet  the  actual  position 
of  Curve  A  on  the  chart  is  higher  than  either  curves  B  or  C. 
If  cumulative  frequency  curves  are  plotted  on  a  "more 
than"  basis  the  position  of  several  curves  on  a  chart  is 
relatively  such  that  the  reader  is  not  confused  so  much  as 
when  curves  are  plotted  on  a  "less  than"  basis 


usual  practice.     The  variables  have  been  reversed,  and  the  independent] 
variable  has  incorrectly  been  made  the  vertical  scale.     Besides  thatj 
the  vertical  scale  reads  downward  instead  of  upward.    In  all  kinds  oi 
curve  plotting  it  is  common  to  have  the  two  scales  begin  with  zerc 
at  the  lower  left-hand  corner  of  the  chart.    Here  the  two  scales  begii 
the  zeros  at  the  upper  left-hand  corner  of  the  chart.    Unless  the  readei 
will  turn  Fig.  154  on  its  side  so  as  to  make  the  two  zeros  at  the  lowei 
left-hand  corner,  he  may  find  great  difficulty  in  interpreting  the  chart.] 
Fig.  155  shows  a  replot  of  the  data  of  Fig.  154.    Here  the  curves  an 
plotted  on  a  "more  than"  basis,  but  it  would  have  been  better  if  th( 


FREQUENCY   CURVES 


179 


words  "more  than",  with  an  arrow,  had  been  placed  at  the  lower 
left-hand  corner  of  the  chart.  In  Fig.  155  a  little  study  will  show 
the  advantages  of  plotting  curves  on  a  "more  than"  basis.  The  reader 
can  see  at  a  glance  from  this  illustration  that  the  wages  for  the  western 
States  are  very  muoh  higher  than  the  wages  in  the  south  Atlantic 
States.  The  position  of  the  curves  one  above  the  other  would  lead 
the  reader  at  once  to  think  of  the  upper  curves  as  showing  higher 
w^ages.  Here  the  upper  curves  do  indicate  the  higher  wages,  but  they 
w^ould  not  do  so  if  they  were  plotted  on  a  "less  than"  basis  instead 
of  on  a  "more  than"  basis.  Though  it  may  cause  some  confusion 
at  first,  it  seems  desirable  as  a  general  rule  that  cumulative  frequency 
curves  should  be  plotted  on  a  "more  than"  basis  rather  than  on  a 
"less  than"  basis. 


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Courtesy  of  W.  S.  Gifford,  American  Telephone  &  Telegraph  Co. 

Fig.  153.    Answering  Time  of  Different  Classes  of  Operators  in  Telephone  Work 

Cumulative  curves  of  this  sort  give  information  in  much  more  condensed  and  clear  form  than  possible  with 
other  methods  of  presentation.  This  particular  chart  is  read  on  a  "less  than"  basis,  as  can  be  seen  by 
the  general  position  of  the  curves  as  related  to  the  scales.  Notice  that  none  of  the  calls  is  answered  in 
less  than  two  seconds 


180 


GRAPHIC    METHODS 


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Fig.  154.    Comparison  of  Earnings  of  Men  Wage  Earners  in  Different  Portions  of 

the  United  States  in  1905 

This  chart  is  almost  hopelessly  confused  because  the  scales  have  been  so  arranged  that  the  two  scale  zeros 
appear  at  the  upper  left-hand  corner  of  the  chart  instead  of  at  the  lower  left-hand  corner.  The  vertical 
scale  reads  downward  when  it  should  read  upward.     See  Fig.  155  for  these  same  data  redjawn 


FREQUENCY   CURVES 


181 


In  Fig.  156  we  have  cumulative  frequency  curves  applied  to  a 
comparison  of  wages  in  different  departments  of  a  corporation.  Here 
again  the  words  "more  than"  and  the  arrow  would  have  been  de- 
sirable at  the  lower  left-hand  corner  of  the  chart.  The  general  position 
of  the  curves  beginning  at  the  upper  left-hand  corner,  however,  assists 
the  reader  to  see  that  these  curves  are  plotted  on  a  "more  than" 
basis.  A  chart  of  this  kind  is  of  great  utility  in  making  a  study  of 
wages.  It  may  be  noticed,  for  instance,  in  the  curve  for  laborers, 
that  there  is  a  very  decided  change  in  the  shape  of  the  curve  at  about 
$9.00  per  week.  Only  62  per  cent  of  these  laborers  make  more  than 
$9.00  per  week  and  but  80  per  cent  of  them  get  more  than  $5.00  per 

Per  Cent 
loo 


20 


•X— X— X— X  — 


7    8    9   10         12  15 

WEEKLY  EARNINGS  -  DOLLARS 

.  «^.     X.  United  States 
N.Atlantic  <^-^-.     S.Atlantic 

N.Central  .— .— .    S. Central 

Western  Alaska 


25 


Fig.  155.  Chart  Showing  What  Percentage  of  the  Wage  Earners  in  Different  Portions 
of  the  United  States  Receive  More  than  any  Specified  Amount  of  Earnings  up  to 
Twenty-Five  Dollars  per  Week 

Here  the  scales  are  correctly  arranged  so  that  the  two  zeros  appear  at  the  lower  left-hand  corner.  The 
plotting  of  these  curves  on  a  "more  than"  basis  causes  curves  which  show  the  largest  earnings  to  appear 
in  their  proper  position  toward  the  top  of  the  chart.  Plotting  of  cumulative  frequency  curves  on  a  "more 
than"  basis  is  usually  desirable,  since  it  reduces  the  chances  for  confusion  to  ths  reader.  This  chart 
could  have  been  improved  if  the  words  "more  than"  and  an  arrow  had  been  placed  at  the  lower  left- 
hand  comer  on  the  general  scheme  of  Fig.  158 


I 


182 


GRAPHIC    METHODS 


O 


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Percent, 

100 

96 
92 
68 
84 
80 
76 
72 
68 
64 
60 
55 
52 
48 
44 
,40 
36 
32 
28 
24 
20 
16 
12 
8 
4 
0 


WAGE  C0:»tPABIS0N  IN  VARIOUS  DEPARTMENIS . 


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DOLLARS. 


Fig.  156.  Comparison  of  Actual  Weekly  Earnings  in  Different  Departments  of  a 
Large  Industrial  Plant  Showing  Percentage  of  Men  in  Each  Department  Receiving 
More  than  Any  Specified  Amount  of  Earnings  per  Week 

This  illustration  was  made  by  photographing  directly  from  the  universally  ruled  paper  shown  also  m 
Figures  57,  103, 130  and  134.  The  scales  and  the  different  titles  were  put  on  the  paper  with  a  typewriter. 
Lack  of  steady  work  caused  many  of  the  laborers  to  get  the  very  small  earnings  shown  by  the  upper 
portion  of  the  curve  marked  "Laborers" 


FREQUENCY   CURVES  183 

week.  The  fact  that  20  per  cent  of  all  the  laborers  earn  less  than 
$5.00  per  week  is  due  to  intermittent  employment  given  laborers  in 
this  particular  business.  As  e$5.00  per  week  is  not  a  living  wage  for 
any  man,  the  shape  of  the  cumulative  curve  for  the  laborers  at  once 
points  out  the  desirability  of  some  change  in  management  by  which 
fewer  men  might  be  employed  and  all  the  men  employed  more  steadily 
than  indicated  by  the  curve  for  laborers  in  Fig.  150.  Since  all  the 
laborers  were  paid  the  same  rate  per  hour,  the  only  possible  explana- 
tion of  the  fact  that  a  large  number  of  men  earn  as  little  as  $5,00  per 
week  must  be  that  the  laborers  were  not  employed  continuously. 
More  continuity  of  employment  for  a  smaller  number  of  laborers 
would,  in  this  particular  case,  have  resulted  in  more  money  being 
paid  on  an  average  to  each  man,  so  that  the  men  would,  to  all  essential 
purposes,  have  received  an  increase  in  pay  even  though  the  hourly 
wage  rate  were  not  increased. 

Though  that  portion  of  the  curves  for  the  office  forces  seen  at  the 
upper  left  corner  of  Fig.  156  appears  somewhat  similar  to  the  curve 
for  laborers,  the  low  earnings  of  a  large  percentage  of  the  office  force 
were  due  to  the  employment  of  office  boys  and  other  young  employees 
who  would  have  a  fair  chance  to  get  a  good  training  and  grow  up 
with  the  business.  Therefore,  the  curves  for  the  office  forces  need 
not  attract  the  same  attention  as  the  curves  for  the  laborers,  who 
are  all  full-grown  men  having  comparatively  little  chance  for  promo- 
tion. 

The  quick  change  at  $11.00-  per  week  in  the  shape  of  the  curve 
relating  to  the  foremen  and  clerks  is  due  to  the  fact  that  some  of  the 
foremen  in  this  business  are  paid  by  the  hour  and  not  by  the  week. 
That  some  of  the  foremen  receive  as  low  as  $6.00  per  week  and  that 
only  93  per  cent  of  the  foremen  receive  over  $11.00  per  week  is  due 
to  the  fact  that  some  of  the  men  were  off  because  of  sickness  or  on 
leave  of  absence.  If  the  attendance  of  these  men  were  more  regular 
the  curves  would  not  have  such  a  decided  peak  at  $11.00  per  week. 
Though  Fig.  156  has  been  plotted  on  a  "more  than"  basis,  the  reader 
may,  if  he  wishes,  read  it  on  a  "less  than"  basis  by  referring  to  the 
right-hand  scale  which  has  zero  at  the  top  instead  of  at  the  bottom 
of  the  page. 

Fig.  156  was  made  directly  from  typewritten  copy  with  only  the 
curves  and  the  marginal  lines  drawn  in  by  hand.  This  same  uni- 
versally  ruled  paper  has  been  referred  to  elsewhere  as  being  con- 


184 


GRAPHIC    METHODS 


venient  for  general  use.  Here  the  paper  is  used  to  indicate  100  per 
cent  in  the  vertical  direction,  and  the  horizontal  scale  is  chosen  for 
data  unrelated  to  time. 


No.  of     Percent  & 
Pieces    No  of  Orders 

2000      lOO 


95 
90 
85 


70 
65 
60 
55 
50 
45 
40 
35 
30 
25 
20 


800 


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SB 

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O    5   10  15  20  25 


75  too 

Size  of  Order  in  Number  of  Pieces 


zoo 


Fig.  157.  Cumulative  Frequency  Curve  Study  of  the  Number  and  the  Size  of  All 
Orders  Handled  During  a  Ten-days  Test  in  a  Certain  Kind  of  Freight-handling 
Work 

The  orders  are  sorted  into  various  classes  or  groups  according  to  the  number  of  pieces  called  for  by  each 

order.     The  limits  for  the  various  classes  were  fixed  by  the  exercise  of  a  little  judgment  and  are  shown 

by  the  vertical  lines  on  the  chart 
Curve  "D"  shows  by  small  circles  the  actual  number  of  orders  found  in  each  group.     The  curve  is  read 

from  the  right-hand  scale 
Curve  "C"  shows  by  small  circles  the  total  number  of  pieces  (or  packages)  carried  by  the  various  orders 

which  are  found  in  each  group.     Curve  "C"  is  read  from  the  left-hand  scale 
Curve  "A"  shows  the  percentage  of  the  total  orders  handled  which  contain  more  than  any  given  number  of 

pieces  considered  on  the  horizontal  scale  of  the  chart 
Curve  "B"  shows  the  percentage  of  the  total  number  of  pieces  carried  by  those  orders  containing  more  than 

any  given  number  of  pieces  considered  on  the  horizontal  scale  of  the  chart 
Curves  "D"  and  "A"  refer  to  the  number  of  orders  or  the  amount  of  clerical  work  while  curves  "C"  and 

"B"  relate  to  the  number  of  packages  handled  or  the  actual  volume  of  business  transacted 

In  Fig.  157  we  have  an  application  of  the  cumulative  frequency 
curve  to  a  class  of  work  which  would  be  extremely  difficult  to  under- 
stand if  the  graphic  method  were  not  used.  In  handling  large  quan- 
tities of  freight  the  different  orders  cover  many  diverse  kinds  of  ma- 
terial, and  the  jobs  vary  from  one  package  up  to  many  thousands  of 
packages  on  one  order.  The  pieces  or  packages  referred  to  here  may  be 
anything  from  a  single  casting  weighing  20  tons  to  a  shipment  of  canned 
goods  with  5,000  boxes  or  cases  on  a  single  shipping  order.  In  the 
long  run,  however,  the  different  classes  of  goods  could  be  averaged, 
and  it  will  be  found  that  in  any  one  locality  there  would  be  but  slight 


FREQUENCY   CURVES  185 

change  from  year  to  year  in  the  average  size  or  weight  of  package 
handled.  The  average  weight  of  package  might  happen  to  be  150 
pounds,  and,  considering  a  whole  year,  there  would  probably  be  very 
little  change  in  the  average  weight  from  month  to  month.  Thus,  for 
our  purpose  here,  the  term  "piece"  or  "package"  refers  simply  to 
the  average  package  handled  in  different  divisions  or  departments 
of  the  work  under  consideration. 

In  order  to  obtain  the  data  regarding  the  orders  referred  to  in 
Fig.  157,  Fig.  158  and  Fig.  159  the  order  slips  are  sorted  into  different 
piles  according  to  some  definitely  thought-out  plan  by  which  there  would 
not  be  too  many  or  too  few  orders  in  any  one  class  or  size  group.  A 
little  preliminary  trial  work  in  sorting  would  show  the  best  places  to 
set  the  class  limits  for  sorting  the  orders  into  separate  piles.  After 
the  orders  have  been  separated  into  piles,  it  is  a  simple  matter  to  count 
the  number  of  orders  in  each  pile  to  obtain  the  data  from  which  curve 
"D"  is  plotted.  It  will  be  noticed  from  the  shape  of  the  curve  that 
the  upper  and  lower  limits  for  each  class  are  well  selected  so  that  there 
is  a  fairly  uniform  decrease  in  the  number  of  orders  in  each  group  as  the 
size  of  the  orders  increases.  The  order  slips  in  the  different  piles  sorted 
according  to  the  size  of  the  order  are  taken  to  an  adding  machine,  and 
addition  made  to  obtain  the  total  number  of  packages  carried  by  the 
combined  orders  found  in  any  one  pile  or  class.  This  gives  the  data  from 
which  curve  "C"  is  plotted.  Though  curve  "D"  shows  a  constantly 
decreasing  number  of  orders  as  the  size  of  the  orders  becomes  greater, 
curve  "C"  proves  that  there  is  an  increasing  number  of  packages 
handled  as  the  orders  grow  larger  toward  the  right-hand  side  of  the 
chart. 

Though  there  are  not  so  many  orders  of  large  size  as  of  small  size, 
the  small  numbers  of  large  orders  nevertheless  carry  many  more  packages 
than  the  large  numbers  of  small  orders.  The  executive  is,  of  course, 
interested  in  revenue  and,  for  revenue  purposes,  as  mentioned  above, 
all  packages  may  be  considered  of  the  same  size.  Revenue  obviously 
depends  upon  the  number  of  packages  handled,  rather  than  on  the 
number  of  orders  handled.  Curve  "C",  then,  shows  at  a  glance  that 
the  small  number  of  large  orders  are  of  much  greater  interest  to  the 
financial  manager  than  the  large  number  of  small  orders. 

Fig.  157  shows  that  during  the  ten-days  test  period  there  were  no 
orders  in  this  particular  class  of  work  which  exceeded  two  hundred 
packages.     Curves  "D"  and  "C",  though  interesting,  do  not  show  all 


186  GRAPHIC   METHODS 

the  information  which  is  desirable  from  the  standpoint  of  management. 
In  order  to  show  up  the  facts  more  clearly,  curves  "A"  and  "B"  are 
plotted  from  the  same  data  as  curves  "D"  and  "C"  respectively. 
Curve  "A"  is  plotted  on  a  cumulative  basis  by  the  same  general  method 
used  for  Fig.  150  and  Fig.  151.  The  total  number  of  orders  for  the 
whole  test  period  is  first  obtained,  and  then  the  cumulative  number 
adding  up  to  any  class-limit  line  on  the  horizontal  scale  of  the  chart  is 
plotted  as  a  percentage  of  the  total  number  of  orders.  Curve  "A" 
joins  the  zero  line  at  200,  showing  that  none  of  the  orders  was  larger 
than  200  packages.  We  can  see  instantly  that,  because  of  the  large 
number  of  small  orders,  only  22  per  cent  of  all  the  orders  handled  were 
larger  than  twenty -five  pieces  per  order.  Only  13  per  cent  of  all  the 
orders  handled  exceeded  fifty  pieces  per  order.  Also,  by  reading  from 
the  vertical  scale  opposite  the  figure  for  50  per  cent,  we  can  see  at  once 
that  only  half  of  all  the  orders  handled  carried  more  than  twelve 
packages. 

In  a  manner  similar  to  that  used  in  making  up  curve  "A",  the  cumu- 
lative curve  "B"  is  made  up  from  the  data  relating  to  the  number  of 
packages  shown  in  curve  "C  ".  It  may  assist  the  reader  to  follow  these 
charts  if  he  keeps  clearly  in  mind  that  curves  "D"  and  "A"  relate  to 
the  actual  number  of  orders  of  various  sizes,  while  curves  "C"  and  "B" 
relate  to  the  number  of  packages,  or  the  amount  of  total  business  car- 
ried by  orders  of  various  sizes.  In  other  words,  curves  "D"  and  "A" 
relate  to  the  amount  of  clerical  work  needed,  while  curves  "C"  and 
"B"  show  the  actual  amount  of  freight-handling  labor  involved  and 
measure  the  amount  of  revenue  earned.  Curve  "B"  thus  shows  that, 
though  there  are  not  many  large  orders,  about  69  per  cent  of  all  the 
revenue  comes  from  those  orders  which  contain  more  than  twenty -five 
packages.  Fifty-six  per  cent  of  the  business  (and  the  revenue)  is  due 
to  orders  containing  more  than  fifty  packages.  Twenty -nine  per  cent 
of  all  of  the  revenue  comes  from  orders  containing  more  than  one  hun- 
dred packages,  yet  none  of  the  revenue  for  the  ten-days  time  considered 
came  from  orders  larger  than  two  hundred  packages,  since  there  were 
no  such  orders  during  the  period. 

It  is  by  reading  curves  *'A"  and  *'B"  in  conjunction  with  each  other 
that  the  manager  may  obtain  the  greatest  information  relating  to  his 
business.  Considering  first  the  orders  which  contain  more  than  ten 
pieces,  curve  "A"  shows  that  55  per  cent  of  the  orders  contain  more 
than  ten  packages,  while  curve  "B "  shows  that  91  per  cent  of  the  reve- 


FREQUENCY   CURVES  187 

niie  comes  from  those  orders  which  are  larger  than  ten  pieces  each.  In 
other  words,  the  manager,  because  of  handhng  so  many  small  orders, 
is  doing  45  per  cent  of  the  total  clerical  work  in  order  to  obtain  9  per 
cent  of  the  revenue.  Since  clerical  w  ork  depends  chiefly  on  the  number 
of  separate  orders,  the  manager  would  be  able  to  reduce  his  clerical 
work  on  this  particular  class  of  orders  somewhere  near  45  per  cent  if 
he  would  refuse  to  handle  orders  of  less  than  ten  packages,  and,  by  such 
a  decision,  he  would  lose  only  9  per  cent  of  his  revenue.  For  most 
businesses,  it  would  pay  handsomely  to  neglect  entirely  9  per  cent  of 
the  revenue  if  45  per  cent  of  the  clerical  work  could  be  avoided.  In 
freight  handling,  the  w^ork  is  of  course  mostly  under  the  jurisdiction 
of  the  Interstate  Commerce  Commission,  so  that  even  if  the  manager 
should  wish  to  refuse  orders  of  small  size,  he  would  not  be  permitted 
to  do  so. 

Though  the  small  orders  must  be  handled  to  give  service  to  the 
public,  a  chart  such  as  Fig.  157  is  nevertheless  of  very  great  assist- 
ance in  pointing  out  the  actual  conditions  existing.  When  it  is 
seen  what  a  large  amount  of  clerical  work  is  involved  in  handling 
orders  which  produce  only  a  small  portion  of  the  revenue,  thought 
could  be  given  to  the  methods  of  handling  small  orders  so  that  the 
small  orders  may  not  cause  any  more  expense  than  absolutely  neces- 
sary. Usually  it  is  possible  to  handle  small  orders  in  a  different  man- 
ner from  the  large  orders,  and,  if  the  true  situation  is  thoroughly 
understood,  small  orders  may  possibly  be  handled  by  methods  which 
will  result  in  much  less  loss  than  would  be  incurred  if  small  orders 
are  handled  by  the  same  methods  used  for  large  orders. 

One  may  see  from  Fig.  157  the  percentages  of  orders  and  of  business 
or  revenue  for  any  size  of  order  which  it  may  be  desired  to  consider. 
Thus,  taking  orders  which  contain  more  than  twenty-five  packages, 
it  can  be  seen  that  22  per  cent  of  all  the  orders  contain  more  than 
twenty-five  packages  and  that  these  orders  carry  69  per  cent  of  the 
total  business  and  bring  in  69  per  cent  of  the  total  revenue.  Though 
these  orders  of  over  twenty -five  packages  do  not  involve  a  large  amount 
of  clerical  work,  they  nevertheless  bring  in  such  a  large  percentage 
of  the  revenue  that  any  dividends  from  this  particular  department 
must  probably  be  paid  from  the  revenue  brought  in  by  orders  in  excess 
of  twenty -five  packages  each. 

The  general  methods  used  in  plotting  Fig.  157  have  been  con- 
sidered at  rather  great  length  because  it  is  felt  that  a  chart  of  this 


188 


GRAPHIC    METHODS 


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Fig.  158.  Cumulative  Frequency  Curve  Study  of  the  Number  and  the  Size  of  All 
Orders  Handled  During  One  Week  in  a  Certain  Kind  of  Freight-handling  Work 
Carried  on  in  Two  Closely-related  Departments 

Curve  "H"  shows  by  small  circles  the  actual  number  of  orders  foimd  in  each  size-of-order-class.  Note  that 
at  the  left  of  the  chart  there  are  numerous  orders  shown  in  each  class  even  though  here  the  limits  of 
each  class  have  been  purposely  made  very  close  together 

Curve  "B"  shows  the  percentage  of  the  total  orders  handled  which  contain  more  than  any  given  number  of 
packages  considered  on  the  horizontal  scale  of  the  chart 

Curves  "A"  and  "C"  are  similar  to  curve  "B"  and  show  subdivisions  of  the  total  number  of  orders  accord- 
ing to  which  of  two  related  departments  handled  the  work 

Curve  "F"  corresponds  with  curve  "B"  but  shows  the  percentage  of  the  total  number  of  pieces  carried  by 
those  orders  containing  more  than  any  given  number  of  pieces  considered  on  the  horizontal  scale  of  the 
chart 

Curves  "G"  and  "E"  are  similar  to  curve  "F"  and  show  subdivisions  in  the  total  number  of  pieces  accord- 
ing to  which  of  two  related  departments  handled  the  work 

One  sub-department  of  the  business  handled  the  orders  portrayed  by  Curve  "A"  and  Curve  "E".  The 
other  sub-department  handled  orders  portrayed  by  Curve  "C"  and  curve  "G".  The  combined  work 
of  the  two  departments  is  shown  by  Curve  "B"  and  Curve  "F" 

The  percentage  of  the  total  number  of  orders  handled  in  each  of  the  two  different  departments,  up  to  any 
size  of  order  read  on  the  horizontal  scale,  may  be  seen  by  considering  the  distances  on  the  chart  above 
and  below  Curve  '''D" 

kind  can  be  of  service  in  a  sales  analysis  for  almost  any  kind  of  busi- 
ness. A  company  selling  fairly  uniform  products — shoes,  for  example 
— could  use  for  the  horizontal  scale  the  actual  number  of  pairs  of 
shoes  contained  on  various  orders  received  for  the  test  period  of,  say, 
a  week  or  a  month.  Companies  having  a  diversified  product,  as  elec- 
trical machinery,  could  best  make  a  chart  of  this  kind  by  basing  the 
horizontal  scale  on  the  actual  value  in  dollars  of  the  various  orders 
received.  Thus,  the  scale  could  be  made  for  orders  in  sizes  larger 
than  $50,  $500,  $1,000,  etc.  If  charts  are  made  for  different  depart- 
ments, very  interesting  comparisons  could  be  made  which  would  bring 


I 


FREQUENCY  CURVES  189 

out  information  valuable  to  a  corporation  executive.  Department 
stores  might  also  have  use  for  charts  on  the  general  plan  of  Fig.  157. 
Different  departments  could  be  considered  by  the  number  of  orders 
of  various  sizes.  As  the  margin  of  profit  in  different  classes  of  goods 
in  different  quantity  sold  would  be  fairly  well  known,  the  manager 
could  get  a  good  idea  as  to  how  much  of  the  time  of  his  sales  force 
was  occupied  in  handling  small  orders,  and  how  much  in  handling 
large  orders. 

Fig.  158  is  drawn  on  the  same  general  scheme  as  Fig.  157.  In 
Fig.  158,  however,  we  have  the  additional  complexity  that  the  freight 
under  consideration  must  be  handled  by  two  distinct  departments 
working  in  very  close  harmony  with  each  other.  As  there  is  a  dif- 
ference in  the  cost  of  doing  the  work  handled  by  the  two  departments, 
the  chart  was  purposely  so  drawn  as  to  show  the  number  of  orders 
and  the  number  of  packages  handled  by  each  of  these  two  distinct 
departments  which  together  do  all  of  the  work  under  consideration. 
Curves  "B"  and  "F"  show  respectively  the  percentage  of  orders 
and  the  percentage  of  business  handled  as  a  whole.  The  other  curves 
show  the  relative  proportions  of  the  orders  and  the  business  done  by 
the  two  departments.  The  position  of  the  curves  on  the  chart  gives 
a  fairly  clear  idea  as  to  whether  the  first  department  or  the  second 
department  handles  the  larger  number  of  orders  and  the  larger  per- 
centage of  the  actual  business. 

^  In  Fig.  153  it  was  shown  that,  because  the  curves  were  plotted 
on  a  *'less  than"  basis,  the  curve  showing  the  smaller  length  of  time 
appears  at  the  top  of  the  chart,  when  one  would  naturally  expect  to 
find  the  smaller  quantities  of  time  recorded  relatively  toward  the 
bottom  of  the  chart.  In  Fig.  158  the  data  are  plotted  on  a  "more 
than"  basis,  and  the  curves  are  seen  in  their  proper  relation  to  each 
other.  Since  the  reader  knows  that  the  chart  is  plotted  on  a  "more 
than"  basis  (as  can  be  seen  by  the  words  "more  than"  at  the  lower 
left-hand  corner  of  the  chart),  he  may  know  instantly  that  the  curves 
relating  to  the  two  different  departments  show  in  their  correct  rela- 
tion to  each  other.  Curves  "G"  and  "C"  relate  to  one  department, 
while  curves  "E"  and  "A"  relate  to  another  department.  Curve 
"C"  appears  above  curve  "A"  on  the  chart,  and  the  reader  may  ac- 
cordingly know  without  detail  study  that  the  department  to  which 
curve  "C"  relates  handles  larger  orders  than  the  department  to 
which  curve  "A"  relates.    In  a  similar  way,  the  upper  portion  of  the 


190  GRAPHIC   METHODS 

chart  shows  that  the  department  to  which  curve  *'G"  relates  handles 
a  larger  percentage  of  the  total  number  of  packages  and  produces  a 
larger  percentage  of  the  revenue  than  the  department  to  which  curve 
"E"  relates.  If  this  chart  had  been  plotted  on  a  "less  than"  basis 
instead  of  on  a  "more  than"  basis,  the  position  of  these  two  curves 
giving  detailed  information  for  the  main  curve  "F"  would  be  exactly 
reversed,  with  curve  "E"  appearing  above  the  heavy  line  "F"  and 
curve  "G"  appearing  below  the  heavy  line. 

It  is  perhaps  well  to  point  out  an  error  in  drafting  which  occurred 
on  Fig.  158.  The  information  most  needed  relates  to  orders  containing 
less  than  three  hundred  packages  each.  It  was,  however,  desired  to 
show  on  the  chart  that  none  of  the  orders  contained  more  than  five 
hundred  packages,  and  the  right-hand  portion  of  the  chart  is  accord- 
ingly shown  with  a  break,  indicating  that  a  section  has  been  omitted. 
As  a  general  rule,  when  making  a  break  in  a  drawing  in  this  manner, 
the  two  portions  on  either  side  of  the  break  are  made  exactly  as  though 
a  piece  of  paper  had  been  torn  out  of  the  middle  of  a  drawing  made 
large  enough  to  include  the  whole  chart.  Fig.  158  is  incorrectly  made 
in  that  the  curve  lines  to  the  right  of  the  figure  300  on  the  horizontal 
scale  have  been  drawn  pointing  down  toward  the  right-hand  corner 
of  the  chart  where  they  show  at  the  left  of  the  break.  These  lines 
would  not  appear  this  way  if  a  piece  of  paper  had  been  torn  out  of 
a  large-size  chart.  The  curve  lines  should  have  continued  up  to  the 
break  in  the  drawing  more  nearly  on  the  slope  seen  in  the  left-hand 
portion  of  the  chart.  The  lines  for  curves  "G",  "F"  and  "E"  would, 
if  correctly  made,  show  much  less  slope  also  at  the  right  of  the  break 
where  they  lead  down  to  the  lower  corner  of  the  chart.  This  error 
is  mentioned  here  simply  that  the  reader  may  have  some  guidance 
if  he  finds  it  necessary  to  make  charts  including  a  break,  similar  to 
that  shown  in  Fig.  158. 

It  is  customary  in  cost-keeping  work  to  make  costs  which  show  only 
an  average  of  the  cost  per  unit,  on  an  average  for  all  orders  completed 
during  a  period  of  time,  say  one  month  or  one  year.  Though  this 
method  of  averaging  all  orders  together  without  respect  to  the  size 
of  the  order  is  sufficiently  accurate  for  many  purposes,  there  are  times 
when  such  a  method  may  gravely  mislead  an  executive.  It  is  almost 
invariably  true  that  small  orders  cost  more  per  unit  of  output  than  or- 
ders of  large  size.  A  man  who  makes  a  selling  price  for  his  work  on 
the  average  cost  of  small  orders  and  large  orders  combined  may  be 


FREQUENCY   CURVES  191 

losing  money  unnecessarily,  because  he  does  not  realize  the  true  cost 
of  work  when  it  is  done  in  only  small  quantities  on  different  orders. 

Fig.  159  proves  the  great  variation  in  the  cost  of  doing  the  w^ork  of 
handling  a  certain  class  of  freight.  The  position  of  the  dots  on  the 
chart  shows  that  work  done  in  orders  of  only  twenty-five  packages 
costs  over  twice  the  average  for  orders  of  four  hundred  or  over.  In 
keeping  track  of  the  cost  of  handling  freight  of  different  kinds  for  a 
large  steamship  terminal  and  warehouse  company"  it  was  found  im- 
possible to  get  reliable  cost  figures  by  averaging,  day  by  day,  the  labor 
cost  of  handling  freight  for  preceding  days.  On  some  days  all  the  orders 
for  one  commodity  might  be  small  orders,  and  on  the  next  day  a  very 
large  quantity  of  that  same  commodity  might  be  handled  all  in  one 
large  order,  so  that  a  gang  of  men  could  work  steadily  all  day  on  that 
one  order.  Naturally  if  a  large  gang  of  men  work  all  day  on  one  order, 
the  cost  per  package  handled  would  be  very  much  less  than  if  several 
different  gangs  were  used  in  handling  numerous  orders  of  only  ten  or 
twenty-five  packages  each.  In  order  to  get  a  clear  view^  of  what  was 
actually  happening,  considerable  study  w^as  given  to  the  problem  and 
the  method  shown  in  Fig.  159  is  the  result. 

It  w^as  decided  to  make  a  pin  board  about  24  by  30  inches,  on  the 
general  scheme  seen  in  Fig.  159,  by  which  separate  orders  could  be 
shown  on  the  chart  by  a  dot  to  represent  each  order  handled.  As  it 
was  desired  to  keep  continuous  records  for  the  chief  commodities,  it 
w^as  not  feasible  to  make  ink  marks  for  it  would  then  be  necessary 
to  start  over  again  frequently  w^ith  a  completely  new  sheet  of  paper. 
To  overcome  this  difficulty,  short  pins  w^ere  used  having  spherical 
glass  heads  only  V32  inch  in  diameter  like  those  seen  at  the  right  in  Fig. 
186.  The  co-ordinate  paper  for  the  chart  itself  was  mounted  on  three 
layers  of  corrugated  straw-board,  having  the  ribs  of  the  middle  layer  at 
right  angles  to  the  ribs  of  the  two  outside  layers,  as  described  in  Chapter 
XII.  A  binding  of  gummed  cloth-tape  around  the  edge  of  the  board 
gave  a  neat  appearance  and  assisted  to  preserve  the  boards  during 
rough  service  and  long  use.  These  boards  were  very  light,  yet  remark- 
ably strong  on  account  of  the  corrugations  running  in  both  directions. 

One  cost  clerk  could  not  possibly  figure  out  the  cost  of  all  orders 
and  all  commodities  handled  each  day.  The  cost  method  w^as  more 
in  the  nature  of  an  automatic  inspection  system  or  check,  so  that  the 
general  efficiency  of  the  work  done  by  numerous  gangs  and  hundreds 
of  men  could  be  judged  by  what  might  be  called  occasional  analyses 


» 


192 


GRAPHIC    METHODS 


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FREQUENCY   CURVES  193 

taken  at  random.  Because  of  the  numerous  commodities  which  were 
handled  on  which  it  was  desirable  to  watch  the  cost  of  freight  handling, 
the  cost  clerk  figured  the  cost  of  any  one  commodity  perhaps  only  one  or 
two  daj^s  in  a  month.  Each  morning  the  cost  clerk  would  sort  out 
all  the  labor  tickets  relating  to  some  one  particular  commodity  which 
had  been  handled  on  the  preceding  day.  The  cost  per  package  would 
be  figured  up  for  each  order  ticket  and,  in  the  board  reserved  for  that 
particular  commodity,  a  tall  pin  would  be  placed  for  each  order  com- 
pleted the  preceding  day,  showing  by  the  position  of  the  pin  the  number 
of  packages  on  the  order  and  the  cost  per  package  of  handling  that 
particular  order.  In  considering  the  pin  marked  8  at  the  right  of  Fig. 
159  we  can  see  that  it  represents  an  order  for  900  packages  and  that  the 
cost  per  package  was  1.1  cent.  After  some  time  in  operating  a  pin 
board  the  position  of  the  various  pins  on  the  board  would  show  in  the 
general  form  of  a  curve,  and  would  indicate  the  cost  of  handling  freight 
of  that  particular  commodity  in  lots  of  different  sizes.  Since  commodi- 
ties received  from  ocean  ships  are  usually  packed  in  some  standard 
size  of  bales,  boxes,  or  bags,  the  pin  method  of  charting  cost  is  a  remark- 
ably reliable  one. 

The  pin  board  can  be  of  great  assistance  to  the  general  superintend- 
ent. As  the  cost  of  handling  certain  orders  for  certain  commodities  for  the 
preceding  day  is  known  about  eleven  o'clock  each  morning,  the  super- 
intendent can  look  over  the  boards  and  note  the  special  tall  pins  which 
show  the  exact  cost  of  various  orders  handled.  Thus,  a  superintendent 
seeing  a  board  of  the  kind  described  would  know  that  on  the  preceding 
day  those  orders  had  been  completed  which  in  Figure  159  are  shown  by 
numbered  dots.  His  attention  would  be  drawn  at  once  to  the  orders 
represented  by  dots  numbered  4,  5,  6  and  8.  These  dots  show  costs 
much  above  the  average  cost  recorded  for  orders  of  those  sizes.  The 
cost  clerk  could  furnish  the  order  numbers  of  these  particular  orders 
and  could  also  give  the  names  of  the  foremen  who  had  been  in  charge 
of  the  work.  The  superintendent  could  then  ask  for  an  explanation 
as  to  why  these  orders  had  cost  much  more  than  the  work  should  have 
cost  for  lots  of  the  size  handled.  Considering  dot  6,  notice  that  the 
average  cost  for  500  packages  is  about  0 .  80  cent,  but  the  order  repre- 
sented by  dot  6  cost  1.50  cent  per  package,  almost  twice  what  it  should 
have  cost.  Though  dot  4  shows  considerably  above  the  average  dots 
for  100-package  lots,  the  percentage  excess  is  not  so  great  as  in  the  case  of 
dot  6.    Dot  4  shows  a  cost  of  about  2.20  cents,  while  the  average  cost 


194  GRAPHIC    METHODS 

for  100  packages  is  about  1.25  cents.  What  the  superintendent  wants 
to  know  is  the  percentage  excess  in  the  cost  above  what  the  chart  shows 
should  be  the  normal  cost  for  any  number  of  packages  under  considera- 
tion. The  chart  brings  out  this  information  very  clearly.  Since  the 
superintendent  can  take  the  matter  up  with  the  various  foremen  before 
noon  of  the  day  after  the  work  was  completed,  the  foremen  soon  get 
the  feeling  that  the  superintendent  knows  what  the  cost  should  be,  and, 
if  anything  happens  to  prevent  work  being  done  cheaply  and  quickly, 
the  foremen  are  likely  to  report  the  conditions  at  once  to  see  if  assistance 
can  be  given  them  so  as  to  keep  the  cost  low. 

After  the  superintendent  has  seen  the  pin  boards  each  morning,  the 
long  pins  represented  by  numbered  dots  in  Fig.  159  are  removed  and  in 
their  places  are  put  the  short  glass-head  pins  having  shanks  so  short 
that  the  pins  may  be  pushed  into  the  straw-board  until  the  head  of  the 
pin  touches  the  co-ordinate  paper.  The  pins  are  then  quite  secure, 
and  the  boards  may  be  worked  upon  and  handled  month  after  month 
without  danger  of  the  pins  becoming  lost  from  the  boards.  The 
ordinary  type  of  tall  pins  or  tacks  used  with  wooden  boards  would  not 
be  at  all  satisfactory  for  this  class  of  work,  as  it  would  be  impossible  to 
work  with  such  boards  containing  thousands  of  tacks  without  knocking 
the  tacks  loose,  so  that  they  would  be  in  a  continuous  process  of  becom- 
ing lost — much  to  the  detriment  of  accuracy  and  to  the  disgust  of  a 
cost  clerk.  The  short  glass-head  pins  pushed  in  until  the  heads  touch 
are  very  convenient  and  they  give  a  thoroughly  accurate  record. 

As  above  mentioned,  cost  boards  of  the  kind  described  would  not 
be  satisfactory  if  made  with  ink  dots  because  the  boards  would  soon 
have  so  many  dots  that  information  would  be  no  longer  easilj^  obtain- 
able. By  using  the  glass-head  pins  it  is  feasible  to  change  the  color  of 
glass  heads  used  on  any  board  each  six  months.  The  position  of  the 
pins  of  different  color  would  then  show  clearly  whether  work  was  being 
done  more  cheaply  than  it  had  been  done  in  preceding  periods  of  time. 
Thus,  if  any  particular  campaign  were  made  to  reduce  the  cost  for 
small  orders  by  handling  small  orders  on  some  different  method  from 
that  previously  used,  the  pins  near  the  left-hand  side  of  the  board  might 
appear  considerably  lower  down  on  the  chart  than  the  pins  of  the  color 
which  had  been  used  in  the  six  months  preceding  the  change  in  method. 

When  the  board  gets  so  full  of  pins  as  to  make  the  pins  crowded  it 
is  a  very  simple  matter  to  remove  from  the  board  all  of  the  pins  which 
were  inserted  in  the  most  remote  period  of  time.     Thus,  it  might  be 


FREQUENCY   CURVES  195 

found  feasible  to  keep  on  the  chart  pins  relating  to  four  different  periods 
of  six  months  each,  so  that  every  six  months  one  color  of  pins  would  be 
removed  from  the  board  and  the  pins  removed  would  be  those  which  had 
been  placed  in  the  board  two  years  previously.  A  board  would  then 
show  at  all  times  the  record  of  cost  in  handling  this  particular  commodi- 
ty during  the  last  two  years.  Boards  used  w^here  pins  must  be  put 
in  and  taken  out  very  often  may  be  faced  with  cork  composition  so  that 
the  pin  holes  may  injure  the  surface  as  little  as  possible.  Where  pins 
are  not  to  be  changed  very  frequently,  the  straw-board  covered  with  a 
layer  of  cloth  before  the  co-ordinate  paper  is  mounted  will  be  found 
entirely  satisfactory. 

In  the  upper  portion  of  Fig.  159  is  shown  a  summary  chart  of  the 
data  contained  on  the  pin  board  itself.  Curve  "C"  is  a  smooth  curve 
drawn  through  the  center  of  gravity  of  all  pins  on  any  vertical  line 
which  shows  the  size  of  order.  It  will  be  noticed  that  the  cost  decreases 
very  little  when  orders  become  larger  than  three  hundred  packages, 
but  for  this  particular  commodity  with  the  methods  of  handling  used, 
the  cost  increases  rapidly  as  orders  decrease  below  three  hundred  pack- 
ages. Knowing  the  revenue  obtained  for  doing  the  work,  it  is  a  simple 
matter  to  determine  from  the  curve  the  smallest  size  of  order  of  this 
commodity  which  can  be  handled  under  average  conditions  without 
incurring  a  loss.  If  the  revenue  for  Fig.  159  were  1.5  cents  per  package 
it  could  be  seen  at  once  that  (since  the  overhead  expenses  are  not  con- 
sidered) there  must  certainly  be  a  dead  loss  on  orders  containing  less 
than  sixty -five  packages  each.  If  the  overhead  expenses  are  taken 
into  account  as  well  as  direct  labor,  there  would  be  shown  a  loss  on 
orders  of  larger  size,  probably  up  to  one  hundred  or  one  hundred  and 
fifty  packages.  Assuming  that  a  loss  occurs  on  all  orders  shown  on 
Fig.  159  up  to  the  size  of  one  hundred  and  fifty  packages  per  order, 
the  number  of  dots  to  the  left  of  the  line  for  150  on  the  horizontal  scale 
indicates  just  how  great  the  total  monetary  loss  would  be. 

Curve  "A"  in  Fig.  159  shows  the  percentage  of  orders  which  contain 
more  than  any  specified  number  of  packages  selected  on  the  horizontal 
scale  of  the  chart.  Curve  *'B"  shows  the  percentage  of  the  total 
packages  which  are  found  in  orders  containing  more  than  any  specified 
number  of  packages  selected  on  the  horizontal  scale  of  the  chart. 
Curve  "A"  indicates  the  amount  of  clerical  work  involved,  and  curve 
"B"  shows  the  amount  of  actual  labor  and  the  amount  of  revenue  in 
exactly  the  same  manner  described  for  Figures  157  and  158. 


196 


GRAPHIC    METHODS 


lOO 


•        •••••     ^c       •  ^k.  •        • 


Curves  "A",  "B"  and  "C"  are  shown  in  Fig.  159  only  by  way  of 
proving  the  utihty  of  the  pin-board  method  of  keeping  costs  where  there 
is  a  large  variation  in  the  size  of  the  orders  worked  upon.  The  illustra- 
tion shows  these  curves  superimposed  on  the  pin  board  only  to  save 

space  in  printing. 

In  Fig.  160  is  shown  a 
chart  which  may  help  to 
make  clearer  the  general 
principles  used  in  drawing 
the  charts  seen  in  Fig.  157, 
Fig.  158  and  Fig.  159.  Fig. 
160  shows  the  appearance 
of  the  curves  if  there  are 
the  same  number  of  orders 
in  each  class  or  group  and 
if  all  classes  or  groups  are 
of  uniform  size.  It  makes 
no  difference  in  the  shape 
of  the  curves  how  many 
orders  there  may  be  if  those 
orders  are  always  uniformly 
distributed  throughout  the 
whole  length  of  the  hori- 
zontal scale  of  the  chart. 
It  would  perhaps  have  been 
better  if  Fig.  160  had  been 
so  drawn  that  the  length 
of  the  vertical  scale  would 
be  the  same  as  the  length 
of  the  horizontal  scale.  The  actual  shape  of  the  curve  line  referring 
to  the  percentage  of  business  or  the  percentage  of  the  total  number 
of  pieces  would  then  be  free  from  any  possible  distortion  which  it  may 
have  received  because  of  the  vertical  scale  being  of  less  total  length 
here  than  the  horizontal  scale. 

It  is  especially  interesting  to  compare  Fig.  160  with  Fig.  159. 
In  Fig.  159  the  reader  may  easily  see  for  himself  that  there  are  many 
more  small  orders  than  there  are  large  orders,  because  the  pins  are 
largely  concentrated  toward  the  left-hand  side  of  the  chart.  It  is 
this  concentration  at  the  left-hand  side  which  has  so  greatly  affected 


Fig.  i6o.  Chart  to  Show  the  Theoretical  Shape 
of  Cumulative  Curves  for  the  Percentage  of 
Total  Orders  and  the  Percentage  of  Total 
Business  if  There  Is  a  Uniform  Number  of 
Orders  in  Each  Class  or  Group 

It  makes  no  difference  in  the  shape  of  the  curves,  as  long  as 
all  classes  contain  the  same  number  of  orders,  whether  there 
is  one  order  or  one  thousand  orders  in  each  class  between 
vertical  lines 

The  straight  line  shows  the  percentage  of  orders  which  contain 
more  than  any  given  number  of  pieces  considered  on  the 
horizontal  scale  of  the  chart 

The  curved  line  shows  the  percentage  of  the  total  number  of 
pieces  carried  by  the  orders  which  contain  more  than  any 
given  number  of  pieces  considered  on  the  horizontal  scale 

If  there  is  not  the  same  number  of  orders  in  all  groups  or  zones 
the  curves  will  take  some  other  shape  and  the  shape  will 
depend  on  the  peculiar  distribution  of  orders  as  may  be 
seen  in  Fig.  157,  Fig.  158  and  Fig.  159 


FREQUENCY   CURVES 


197 


lOO 


90 


80 


70 


the  shape  of  curve  "A"  and  curve  "B"  in  Fig.  159.  By  comparing 
Fig.  160,  we  can  see  that  if  the  distribution  of  orders  in  Fig.  159  had 
been  uniform,  curve  *'A"  would  have  been  a  straight  diagonal  hue 
and  curve  "B"  would  have  been  a  curved  line  bowed  upward  instead 
of  bowed  downward. 

Though  Fig.  161 
somewhat  resembles 
Fig.  160,  it  is  never- 
theless constructed  on 
an  entirely  different 
plan.  In  Figs.  157, 
158,  159  and  160  the 
independent  variable 
related  only  to  size 
of  order.  For  charts 
of  the  type  shown  in 
Fig.  160  the  inde- 
pendent variable  is  a 
percentage.  The  de- 
pendent variable  is 
also  expressed  as  a 
percentage. 

Imagine  the  whole 
population  placed  in 
a  long  line  and  ranked 
according  to  income. 
The  people  in  this 
line  could  be  counted 
off  into  several  equal 
groups   so    that  each 


J3 

§60 


o  50 


o40 


30 


20 


ID 


7 

, 

..V 

,.v 

/ 

/ 

/ 

« 

V 

/ 

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/ 

/ 

/ 

.V 
.V 
V 

/ 

/, 
:/ 
> 

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^ 

10 


20 


30        40        50        60       70 

Percents  of  Total  Income 


60       do       too 


EQUALITY     PRUSSIA  1892.  PRUSSIA  1901 

M.  O.  Lorem,  in  the  Publications,  the  American  Statistical  Assn. 

Fig.  i6i.  Curves  to  Show  the  Percentages  of  the  Total 
Population  of  Prussia  in  1892  and  in  190 1  that  Re- 
ceived Various  Percentages  of  the  Total  Income  as 
Considered  on  the  Horizontal  Scale 

If  incomes  were  all  equal  the  relation  of  population  and  income  would  be 
expressed  by  the  straight  diagonal  line.  The  amount  of  inequality 
between  various  incomes  is  shown  by  the  amount  the  curve  diverges 
from  the  straight  line.  There  was  greater  inequality  of  incomes  in 
Prussia  in  1901  than  in  1892 


group  would  contain  say  10  per  cent  of  the  total  number.  It  would 
then  be  simple  to  compute  the  mcome  of  each  group  as  a  percentage 
of  the  combined  income  for  all  groups.  The  resulting  group  percentages 
would  be  plotted  cumulatively  as  the  dependent  variable  on  a  chart 
for  which  percentages  of  population  would  be  the  independent  vari- 
able. Fig.  161  unfortunately  shows  the  independent  variable  used 
for  the  vertical  scale.  A  better  arrangement  may  be  seen  by  observ- 
ing the  illustration  through  the  back  of  the  paper  with  the  two  zeros 
appearing  at  the  lower  left-hand  corner. 


198 


GRAPHIC    METHODS 


Diagrams  made  on  the  scheme  of  Fig.  161  are  of  very  great  assist- 
ance in  studying  such  matters  as  the  distribution  of  wealth  for  any 
country.  The  subject  of  wealth  distribution  is  so  complex  that  unless 
data  are  expressed  graphically  there  would  be  very  serious  difficulty 
in  getting  a  true  understanding  and  appreciation  of  the  different 
factors  involved.  In  Fig.  161  we  have  the  curves  for  two  widely  sep- 
arated years  plotted  side  by  side,  so  that  we  may  tell  from  the  general 
shape  of  the  curves  whether  the  distribution  of  wealth  is  approaching 
uniformity  of  tending  in  the  direction  of  great  concentration  in  the 
hands  of  a  few  people.  The  more  nearly  the  curve  approaches  a  straight 
line  the  more  nearly  wealth  is  distributed  uniformly  among  all  the 


14. 


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O      ^OOO    2,000    3,000    4OOO    5,000    6,000    7,000    SpOO    9000    lO.OOO 

Rating    of"  Truck    in   Pounds 
•  Report  by  Operator  a  Estimate  by    Manufacturer 

»  Average  reported  Figure 

H.  F.  Thomson,  Massachusetts  Institute  of  Technology,  Vehicle  Research 

Fig.  162.     Cost  of  Gasoline  in  Cents  per  Truck-Mile  for  Different  Sizes  of  Motor 

Trucks 

Since  motor  trucks  are  rated  by  the  manufacturers  in  multiples  of  1,000  pounds,  the  dots  representing  the 
records  of  different  trucks  naturally  fall  on  the  lines  spaced  by  1,000-pound  intervals  on  the  chart. 
The  solid  line  is  drawn  through  points  at  the  "center  of  gravity"  of  all  dots  for  any  vertical  line  on  the 
chart  and  represents  the  average  condition  as  reported  by  truck  operators.  The  dotted  line  is  drawn 
through  points  on  the  chart  for  data  furnished  by  the  manufacturer  as  his  estimate  of  good  practice 

A  curve  of  this  general  type,  proving  a  close  relationship  between  two  variables,  may  be  called  a  correlation 


■  CORRELATION  199 

members  of  the  population.  In  Fig.  161  the  Hne  was  more  bowed 
in  the  later  year  than  in  the  earlier  year,  and  the  conclusion  may  ac- 
cordingly be  drawn  that  wealth  in  Prussia  tended  toward  further  con- 
centration in  those  years  intervening  between  1892  and  1901. 

In  Fig.  162  a  study  has  been  made  to  see  how  the  gasoline  con- 
sumption of  motor  trucks  varies  in  trucks  of  different  sizes.  The  hori- 
zontal scale  shows  the  rated  size  in  pounds  of  the  trucks  under  con- 
sideration. On  the  vertical  scale,  the  cost  of  gasoline  is  given  in  cents 
per  car  mile.  The  data  of  the  different  motor  trucks  were  indicated 
by  separate  dots  on  the  chart.  The  solid  line  was  then  drawn  through 
a  point  which  represents  the  center  of  gravity  of  all  the  dots  on  each 
vertical  line.  The  total  number  of  dots  on  this  chart  is  rather  small. 
Too  much  dependence  cannot  be  placed  in  the  resulting  curve,  as 
special  conditions  may  have  affected  some  of  the  records  so  as  to 
cause  the  dots  to  be  misleading.  Thus,  considering  the  two  dots 
which  are  given  for  trucks  of  2,000-pounds  capacity,  it  will  be  noticed 
that  both  of  these  dots  are  far  below  the  position  on  the  chart  which 
one  would  expect  the  average  to  occupy  if  one  should  judge  by  the  gen- 
eral tendency  of  the  curve  as  a  whole.  It  may  have  happened  that 
the  particular  trucks  which  these  two  dots  represent  were  run  with 
very  light  loads,  thus  making  the  gasoline  consumption  lower  than 
would  naturally  be  expected  for  trucks  of  that  size.  In  Fig.  162  the 
object  is  to  determine  what  relation,  if  any,  exists  between  the  cost 
for  gasoline  and  the  size  of  the  truck. 

"Correlation"  is  a  term  used  to  express  the  relation  which  exists 
between  two  series  or  groups  of  data  where  there  is  a  causal  con- 
nection. In  order  to  have  correlation  it  is  not  enough  that  the  two 
sets  of  data  should  both  increase  or  decrease  simultaneously.  For 
correlation  it  is  necessary  that  one  set  of  facts  should  have  some  defi- 
nite causal  dependence  upon  the  other  set,  as  seen  in  Fig.  162. 

Correlation  studies  can  frequently  be  of  assistance  in  business  prob- 
lems. A  manufacturer  of  machinery  has  recently  revised  many  of 
his  manufacturing  and  selling  policies  from  the  information  obtained 
from  a  chart  showing  the  relations  of  cost  and  selling  price  of  his 
equipment  to  the  actual  size  of  the  equipment.  On  the  horizontal 
scale  of  charts  used  for  this  study  the  size  of  the  apparatus  was  shown 
according  to  its  actual  working  capacity.  In  a  vertical  direction  a 
scale  was  selected  for  the  cost  of  the  apparatus  and  for  its  selling 
price.     Dots  were  then  placed  on  the  chart  in  a  manner  similar  to 


200  GRAPHIC    METHODS 

Fig.  162,  and  a  line  was  drawn  on  the  chart  through  the  different  dots 
representing  the  factory  cost  of  the  machinery.  The  hne  was  not  at 
all  straight  and  the  chief  executive  spent  much  time  in  finding  out 
why  there  were  so  many  variations  from  uniformity.  He  found, 
among  other  things,  that  some  of  his  machinery  had  not  been  re- 
designed for  several  years,  and  that  the  weight  of  material  used  was 
much  greater  than  necessary  when  taking  into  account  the  greater 
strength  of  steel  and  iron  made  by  modern  processes.  Though  mate- 
rials of  the  modern  kind  were  being  used  to  a  large  extent  in  his  ma- 
chinery, the  weight  of  material  had  not  been  reduced  and  there  was 
more  weight  of  employed  material  than  was  actually  necessary  if  new 
designs  were  made.  Another  cause  for  fluctuation  in  the  curve  line 
was  found  in  the  quantities  in  which  the  product  was  manufactured. 
Some  sizes  of  apparatus  were  particularly  suitable  to  the  public, 
and  on  these  sizes  the  quantities  were  much  larger  than  on  other 
sizes.  The  sizes  more  commonly  sold  were  naturally  better  equipped 
with  jigs  and  tools  than  other  sizes,  and  for  that  reason  the  cost  was 
lower  than  would  otherwise  be  expected.  After  the  cost  curves  had 
been  thoroughly  studied  for  different  kinds  of  apparatus,  the  selling- 
price  curves  were  drawn  in  on  the  same  sheets.  It  was  found  that 
for  selling  prices,  also,  there  were  numerous  inconsistencies  which 
could  be  corrected  with  advantage  to  the  company.  Though  some  of 
the  peaks  and  valleys  of  the  selling-price  correlation  curves  were  to 
be  expected,  there  was  no  justification  for  others  and  a  little  concen- 
trated study  brought  forth  methods  by  which  the  selling-price  curves 
could  be  changed  materially  with  advantage  to  both  the  producer 
and  the  consumer. 

In  the  study  of  physics  and  of  experimental  engineering,  there  are 
many  times  when  a  correlation  curve  is  of  assistance  in  the  discovery 
and  understanding  of  the  laws  of  nature.  For  Fig.  163,  many  ob- 
servations were  made  and  recorded  on  a  sheet  of  co-ordinate  paper. 
After  sufficient  observations  had  been  made  throughout  the  whole 
range  of  the  horizontal  scale,  smooth  curves  were  drawn  which  would 
most  nearly  represent  the  various  dots  plotted.  In  drawing  curves 
of  this  kind,  care  should  be  taken  to  have  each  portion  of  the  curve 
as  nearly  as  possible  at  the  center  of  gravity  of  the  dots  in  any  vertical 
section  of  the  chart.  Accuracy  is  not  necessarily  obtained  by  having 
the  same  number  of  dots  on  either  side  of  the  curve.  If  there  are 
only  three  dots  at  some  vertical  line,  it  may  be  that  two  of  these  dots 


CORRELATION 


201 


would  be  close  together  and  their  combined  weight  must  be  considered 
as  compared  with  one  dot  which  may  be  some  distance  away.  As  a 
simple  rule,  consider  the  dots  in  any  vertical  section  of  the  chart  as 
though  arranged  on  a  see-saw,  as  used  by  children,  and  then  shift 
the  point  through  which  the  curve  line  is  to  be  drawn  so  that  the 
see-saw  will  just  balance  evenly. 

80-,000rl600- 


70,000 


10,000 


2         3         4         5         6         7         8         9       ;10        11        12 
Velocity  of  circulating  water —ft.  per  sec.  -^Fw 

Geo.  A.  OTTot,  in  Jovrnal  American  Society  of  Mechanical  Engineers 

Fig.  163.    Relation  of  the  Rate  of  Heat  Transmission  to  the 
Velocity  of  the  Circulating  Water  in  Surface  Condensers 

Correlation  charts  of  this  type  have  sometimes  been  called  "shot-gun  diagrams" 
The  investigator  makes  a  dot  for  each  observation  recorded,  and  then  judges 
from  the  arrangement  of  the  dots  whether  there  is  any  general  law  expressing 
a  relation  between  the  two  variables  studied 

Curves  like  those  seen  in  Fig.  163  may  be  sketched  in  free-hand, 
or  they  may  be  much  more  conveniently  drawn  by  using  the  irregular 
or  so-called  "French  curves"  which  may  be  obtained  in  any  store 
selling  drafting  instruments  or  artists'  materials.  As  it  frequently 
happens  that  an  irregular  curve  available  does  not  exactly  fit  the  dots 
through  which  the  curve  line  is  to  be  drawn,  care  must  be  taken  to 


202 


GRAPHIC    METHODS 


shift  the  irregular  curve  along  and  draw  only  short  portions  of  the 
curve  line  at  any  one  stroke  of  the  pencil  or  pen.  Care  in  shifting  the 
irregular  curve  will  permit  drawing  a  clean,  smooth  curve  line,  even 
though  the  irregular  curve  used  is  quite  different  in  shape  from  the 
curve  line  which  is  drawn. 


69- 

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S2   63   S4   69 


ee    69   60    61    6S    63   64 

i[other'$  Span  (  =  lf)  in  itwhes. 


Karl  Pearson  in  "BiometTika" 


Fig.  164.  Correlation  Curve  Showing  Probable  Span  of  a  Daughter  from  Finger  Tip 
to  Finger  Tip,  for  any  Given  Span  of  the  Mother.  1,370  Cases  were  Studied 
in  Making  up  this  Chart 

Here  the  dots  for  the  1,370  observations  are  not  all  shown.  The  dots  seen  represent  the  averages  of  all 
cases  studied  in  each  1-inch  range  of  mother's  span  according  to  the  horizontal  scale.  The  curve  line 
is  then  drawn  through  these  dots.  Instead  of  using  the  curve  line,  the  mathematical  relation  may  be 
expressed  by  the  formula  D  =  34 .  18  +  .473  M 

This  chart  would  have  been  easier  to  interpret  clearly  if  both  the  vertical  and  the  horizontal  scales  began 
with  the  same  figure,  say  51  inches.  The  reader  is  not  apt  to  notice  that  the  vertical  scale  here  begins 
at  58  while  the  horizontal  scale  begins  at  51 

Curves  like  those  seen  in  Fig.  163  are  properly  drawn  as  smooth 
curves  because  they  are  based  upon  some  definite  laws  of  nature. 
It  is  only  because  of  the  crudity  of  the  observations  of  mankind  that 
the  dots  are  so  widely  scattered.  If  human  knowledge  were  sufiicient 
to  obtain  measurements  with  exactness,  curves  for  data  relating  to 
the  laws  of  nature  would  fall  exactly  on  points  plotted  according  to 
the  observations  and  there  would  be  no  difficulty  in  getting  smooth 
curves.  The  curves  in  this  book  are  nearly  all  plotted  from  statistical 
data  for  which  there  are  ordinarily  some  hundreds  of  variables,  of 
which  many  do  not  follow  any  definite  laws  of  nature.  For  most 
statistical  work  it  is  much  better  to  join  the  points  showing  the  ob- 
servations by   straight   lines   without  any   attempt  to   draw   smooth 


CORRELATION  203 

curves.  Smooth  curves  would  by  their  smoothness  imply  a  degree 
of  accuracy  in  the  data  much  greater  than  would  ordinarily  be  justi- 
fiable. By  using  the  straight  lines  instead  of  the  smooth  curves  to 
connect  points,  the  reader  is  warned  that  the  chart  represents  facts 
as  found,  rather  than  facts  which  are  assumed  to  be  in  accordance 
with  any  definite  laws.  Where  smooth  curves  are  proper,  as  in  Fig. 
1C3,  it  is  feasible  to  have  a  mathematical  formula  to  represent  the 
shape  of  the  smooth  curve.  As  the  determination  of  mathematical 
formulas  to  suit  the  shape  of  any  curve  is  a  whole  study  in  itself,  there 
will  be  no  attempt  to  cover  that  subject  in  this  book. 

Biologists  have  constant  use  for  correlation  curves.  Fig.  164 
shows  a  curve  used  in  the  solution  of  a  typical  problem  such  as  biolo- 
gists are  constantly  attacking.  It  was  desired  here  to  find  out  what 
laws  govern  the  physical  characteristics  of  the  offspring  when  certain 
characteristics  are  found  in  the  mother.  In  all,  1,370  cases  were 
measured,  both  mother  and  daughter,  to  get  the  data  from  which 
Fig.  164  was  plotted.  All  the  cases  were  classed  according  to  the 
span  of  the  mother,  with  the  class  limits  made  1  inch  apart.  A  single 
point  was  plotted  on  the  chart  as  an  average  for  each  class.  A  curve 
line  was  then  drawn  so  as  to  represent  most  closely  the  data  shown 
on  the  chart,  and  it  is  seen  that  the  curve  is  a  straight  line.  There  were 
naturally  fewer  observations  at  either  end  of  the  chart,  for  the  very 
small  spans  and  for  the  very  large  spans,  than  for  the  intermediate 
spans.  It  was  probably  because  of  the  small  number  of  observations 
at  either  end  of  the  curve  that  the  dots  there  are  so  far  away  from  the 
curve  line.  If  more  numerous  observations  were  taken  it  is  probable 
that  all  the  averages  would  fall  more  closely  on  the  curve  line  than  seen 
in  Fig.  164. 

The  ordinary  course  of  procedure  in  making  a  correlation  chart 
is  to  plot  all  the  observations  by  the  method  seen  in  Fig.  163.  Some- 
times, however,  the  observations  are  so  many  as  to  make  an  extremely 
confusing  chart  if  the  observations  are  shown  in  the  form  of  separate 
dots.  In  Fig.  164  the  observations  in  any  1-inch  class  have  been 
averaged  and  all  the  observations  in  one  class  are  represented  by  a 
single  dot.  In  Fig.  165  the  dots  would  be  very  numerous,  so  numerous 
as  to  make  it  not  feasible  to  show  them  on  a  small  size  chart.  For 
Fig.  165  it  was  desired  to  show  the  maximum  income  and  the  minimum 
income,  as  well  as  the  average  income.  Instead  of  showing  all  the 
dots  on  the  chart,  cross-hatching  was  used  to  represent  the  area  in 


204 


GRAPHIC   METHODS 


Fig.  165.  Income  of  Graduates  of  Worcester  Poly- 
technic Institute  at  Various  Years  After  Graduation 

Instead  of  showing  hundreds  of  dots  to  represent  the  data  received  from 
different  graduates,  the  chart  was  simplified  by  shading  the  area 
representing  the  range  of  income.  The  shading  thus  shows  the  maxi- 
mum and  the  minimum  incomes.  This  general  method  is  a  worthy 
one 


which  the  dots  fell.  The  upper  edge  of  the  cross-hatching  shows  the 
maximum  of  the  incomes,  and  the  lower  limit  of  the  cross-hatching 
shows  the  minimum  of  the  incomes  reported  for  different  years  after 
graduation.  The  reader  can  thus  get  the  whole  story  at  a  glance 
without  being  con- 
fused by  the  com- 
plexity which  would 
result  if  all  the  dots 
were  shown.  Atten- 
tion should  be  called 
to  the  fact  that  the 
curve  of  average  in- 

r>r\m*i        folic        miir»tl  YEARS    after    receipt  of  B.S.  DEGREE  OR  COMPLETION  OF  FOUR  YEAR  COURSE 

CUUIC       IttllS       lllUCll  Courtesy  of  Data,  Chicago 

closer  to  the  bottom 

of  the    shaded   area 

than  to  the  top  of  the 

area.  This  fact  shows 

that,    though    there 

are  several  graduates  getting  high   salaries  much   above  the  average 

income,  nevertheless,  if  all  of  the  dots  were  shown,  most  of  the  dots 

would  fall  below  the  average  line  rather  than  above  the  average  line. 

A  few  extremely  large  incomes  near  the  maximum  line  of  the  chart  could 

greatly  raise  the  average  line  but  still  most  of  the  dots  would  be  found 

beneath  the  average. 

Fig.  166  is  a  very  interesting  correlation  chart.  Here  a  single  dot 
has  been  used  for  each  observation  and  the  dots  are  shown  in  the 
chart.  Instead  of  showing  each  dot  in  its  exact  position,  the  dots 
have  been  grouped  so  that  all  the  dots  are  arranged  uniformly  inside 
of  squares  formed  by  co-ordinate  lines  spaced  10  units  apart  in  the 
scales  for  examination  marks.  Classification  by  class  limits  10  units 
apart  on  the  scale  of  marks  is  sufficiently  accurate  for  all  practical 
purposes,  as  is  proved  by  the  gradual  change  in  shading  on  the  chart 
as  a  whole.  With  few  observations  it  might  be  desirable  to  show  dots  on 
the  chart  to  actual  scale  rather  than  in  classes  by  tens. 

Ordinarily  a  line  drawn  like  the  heavy  wavy  line  in  Fig.  166  would 
be  so  placed  that  the  points  on  the  line  would  be  at  the  center  of 
gravity  for  the  dots  vertically  on  either  side  of  the  line.  Here,  however, 
the  line  is  so  drawn  that  there  are  an  equal  number  of  dots  on  either 
side  of  the  line,  at  right  angles  to  it  at  any  point  throughout  its  course. 


CORRELATION 


205 


Notice  that  in  the  upper  portion  of  the  chart  the  Hne  shifts  across  the 
equahty  Hne,  showing  that  some  of  the  more  brilHant  girls  obtain 
higher  marks  in  arithmetic  than  they  do  in  Enghsh.  The  lower  por- 
tion of  the  chart  shows  that  the  larger  number  of  girls  get  considerably 
better  marks  in  English  than  in  arithmetic,  and  that  this  is  a  general 
condition  to  be  expected.  In  the  case  of  those  girls  who  do  well  in 
both  English  and  arithmetic,  there  seems  to  be  improved  facility  in  the 
field  of  arithmetic. 


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English  Marks — ► 

Data  0/  W.  Garnett  in  the  Journal  of  the  Royal  Statistical  Society,  1910 

Fig.  i66.    Examination  Marks  Obtained  by  9,396  School  Girls  in  England 

Each  girl  is  represented  by  one  dot  showing  to  scale  the  grade  in  English  and  the  grade  in  arithmetic.  The 
dots  are  arranged  uniformly  inside  of  squares  formed  by  co-ordinate  lines  spaced  ten  units  apart  in  the 
scales  for  marks.  The  straight  diagonal  line  drawn  from  zero  shows  equal  ability  in  the  two  studies. 
The  heavy  wavy  line  is  drawn  through  points  having  an  equal  number  of  girls  represented  on  either 
side  of  the  line,  and  its  position  proves  that  girls  have  much  more  ability  in  English  than  in  arithmetic. 


206 


GRAPHIC    METHODS 


The  data  of  Fig.  166  are  shown  by  another  method  in  Fig.  167. 
Though  Fig.  167  appears  to  represent  a  sohd  model,  there  was  iri  reahty 
no  sohd  model  made  in  order  to  obtain  this  illustration.  By  using  iso- 
metric paper  a  chart  like  Fig.  167  can  be  made  with  comparatively 
little  work.  Isometric  paper  has  lines  ruled  on  the  paper  right  and  left 
at  an  angle  of  30  degrees  to  the  horizontal.  By  selecting  a  vertical 
scale  to  portray  by  separate  columns  the  number  of  girls  represented 
in  any  square  of  Fig.  166,  it  becomes  a  comparatively  simple  matter  to 
draw  the  illustration.  The  various  necessary  lines  can  be  drawn  free- 
hand in  pencil  on  top  of  the  isometric  co-ordinate  ruling,  until  the  chart 
is  completed;  then  the  various  lines  can  be  inked  in  to  get  the  final 
effect  seen  in  Fig.  167.  The  total  number  of  girls  represented  in  any 
column  is  shown  by  the  figures  at  the  top  of  the  column. 


S0\ 


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Data  of  \V.  Garnetl  in  the  Journal  of  the  Royal  Statistical  Society,  1910 

Fig.  167.    Examination  Marks  Obtained  by  9,396  School  Girls  in  England 

This  illustration  was  made  from  the  same  data  as  Fig.  166.     Here  the  number  of  girls  in  any  square  is  shown 

by  the  height  of  the  vertical  column  drawn  to  scale. 
The  arrangement  of  scales  here  is  different  from  that  in  Fig.  166  as  will  be  noticed  by  observing  the  direction 

of  the  arrows 


CORRELATION  207 

The  reader  should  note  carefully  that  the  scale  arrangement  of 
Fig.  167  is  entirely  different  from  that  used  in  Fig.  166.  In  Fig.  166,  the 
two  zeros  fall  together  as  they  ordinarily  should  do  in  chart  work  of 
this  sort.  In  Fig.  167,  however,  the  two  scale  zeros  are  not  together 
and  the  reader  is  accordingly  prevented  from  interpreting  Fig.  167 
directly  from  the  location  of  dots  seen  in  Fig.  166.  It  w^ould  seem  as 
though  a  better  chart  could  have  been  made  if  the  isometric  chart, 
instead  of  being  as  in  Fig.  167,  had  been  arranged  with  the  two  zeros 
together.  Such  an  arrangement  w^ould  have  permitted  easier  interpre- 
tation, for  the  reader  would  have  secured  a  more  close  similarity 
to  Fig.  166.  Another  possible  arrangement  which  would  have  been 
better  than  that  used  in  Fig.  167  would  put  the  two  100  per  cent  marks 
of  the  scale  together,  with  the  zero  marks  at  the  diagonally  opposite 
corners.  A  chart  of  this  nature  would  show  as  two  mountain  peaks, 
one  on  each  side,  with  a  valley  in  the  center. 

Where  an  actual  model  is  desired  more  than  an  illustration,  a  very 
convenient,  yet  cheap,  arrangement  can  be  had  by  stringing  beads  on 
separate  wires,  each  mounted  in  the  center  of  ruled  spaces,  like  those 
shown  in  Fig.  166.  The  number  of  beads  on  each  wire  can  represent 
to  scale  the  data  for  the  particular  square  at  the  center  of  which  the 
bead  wire  is  placed.  The  heights  of  the  columns  of  beads  on  the  differ- 
ent wires  would  then  show  clearly  the  facts  for  any  one  section  of  the 
field  in  a  manner  similar  to  that  of  Fig.  167.  The  beads  would  probably 
be  more  generally  understood  by  an  untrained  person  than  the  isometric 
drawing  of  Fig.  167,  and  it  is  for  this  reason  that  the  scheme  is  mentioned 
here.  The  arrangement  by  columns  seen  in  Fig.  167  is  satisfactory 
for  the  trained  reader,  but  the  separate  beads  on  wires  would  probably 
give  a  less  abstract  impression,  more  easily  grasped  by  the  average 
person. 


Chapter  XI 
MAP  PRESENTATIONS 

MAPS   marked,  colored,  or  shaded  in  different  ways,  or  used  in 
conjunction  with  pins  or  other  signals,  form  one  of  the  most 
convenient  means  of  conveying  information.     Such  maps  may 
be  used  to  advantage  in  a  surprising  variety  of  ways,  only  a  few  of 
which  can  be  mentioned  here. 

Engineers  who  have  with  great  labor  prepared  complete  plans, 
specifications,  and  estimates  for  some  proposed  improvement  are  fre- 
quently disappointed  that  they  cannot  arouse  enough  enthusiasm  in 
the  proposed  scheme  to  obtain  the  approval  of  the  government  or 
municipal  officials,  or  members  of  a  corporation  board  of  directors,  who 
must  vote  in  favor  of  the  plan  and  appropriate  the  money  necessary  to 
carry  it  into  effect.  It  is  always  difficult  to  get  non-technical  persons 
to  take  an  interest  in  proposals  which  are  shown  only  by  blue  prints 
and  ordinary  maps.  Architects  realize  this  so  well  that  it  is  common 
practice  among  them  to  submit  carefully  prepared  wash-drawings  to 
show  the  appearance  of  the  building  for  which  they  are  submitting 
plans.  Most  engineering  work  cannot  be  easily  represented  by  wash- 
drawings,  and  the  engineer  is  accordingly  somewhat  handicapped  as 
compared  with  the  architect  in  arousing  interest  in  his  project. 

Fig.  168  shows  a  picture  developed  by  H.  W.  Holmes,  Chief  of  the 
Bureau  of  Highways  and  Bridges,  of  the  city  of  Portland,  Ore'gon,  to 
present  his  plans  advantageously  to  the  common  council  and  the  tax- 
payers to  obtain  their  approval  for  the  expenditure.  A  photograph 
of  the  actual  site  of  the  bridge  was  made,  and  then  the  picture  of  the 
bridge  was  drawn  in  by  hand  on  the  photograph.  Most  engineers 
submitting  plans  for  an  improvement  of  this  kind  would  send  only  a 
set  of  blue  prints  and  perhaps  a  map  marked  to  show  the  location  of 
the  proposed  bridge.  A  picture  like  Fig.  168  can  be  used  in  conjunc- 
tion with  a  map  if  desired.     Certainly  a  proposition  carefully  worked 

208 


MAP    PRESENTATIONS 


209 


up  and  submitted,  as  was  the 
proposed  bridge  shown  in  Fig. 
168,  is  more  Hkely  to  receive 
favorable  consideration  than 
one  in  which  only  the  ordi- 
nary blue  prints  and  maps  are 
used. 

If  maps  must  be  printed 
in  a  report,  a  book,  or  a  maga- 
zine, it  is  usually  necessary, 
on  account  of  the  high  cost  of 
color  printing,  to  use  some 
arrangement  of  black  ink  for 
shading  those  areas  which  on 
a  single  map  would  ordinarily 
be  colored  by  hand.  Fig.  169 
is  a  sample  of  what  can  be 
done  without  the  use  of  color. 
If  the  drawing  is  made  con- 
siderably larger  than  the  fin- 
ished illustration,  the  shading 
can  be  put  on  effectively  by 
hand  work.  Mechanical  shad- 
ing by  the  Ben  Day  process, 
as  regularly  used  by  good  en- 
gravers, gives  excellent  results 
but  its  use  makes  zinc  cuts 
rather  expensive.  Many  illus- 
trations in  this  book  are  made 
by  the  Ben  Day  process.  Any- 
one wishing  to  know  more 
about  the  possibilities  of  this 
process  should  look  up  Fig. 
233  or  consult  the  engraver 
who  is  to  make  the  line  cuts. 

Often  the  matter  to  be 
presented  calls  for  maps  of 
a  large  size,  which  can  be 
obtained  only  at  considerable 


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210 


GRAPHIC    METHODS 


%    \    0  /O  20  30  40 
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i.    I    ScaleinMiles 


Plains 


Engineering  Record 


Fig.  169. 


Drainage  Area  of  the  Canadian 
River,  New  Mexico 

Areas  of  different  kinds  may  be  distinguished  on  maps 
by  various  classes  of  shading  when  color  printing 
is  not  available 


expense.  Sometimes  only  one 
map  is  available  when  a  variety 
of  plans  must  be  presented. 
In  such  cases,  it  is  not  feasible 
to  draw  plans  for  new  con- 
struction work,  or  alternative 
working  schemes,  on  the  map 
itself.  Most  draughtsmen  put 
the  map  on  a  large  drawing 
board  and  then  draw  the  new 
constructions  on  separate  sheets 
of  tracing  cloth.  The  tracing 
cloth  is  not  very  transparent, 
however,  and  it  will  not  help 
greatly  to  get  a  project  voted 
upon  favorably  if  the  plan  must 
be  presented  to  a  board  of  direc- 
tors on  tracing-cloth  drawings 
with  the  map  itself  only  very 
dimly  visible  through  the  trac- 
ing cloth.  A  much  more  effective  scheme  is  to  use  a  sheet  of  almost 
transparent  celluloid  made  with  a  rough  surface  that  will  take  drawing 
ink  fairly  well.  The  different  alternative  plans  may  then  be  drawn  on 
the  celluloid  in  colored  inks,  and  the  different  sheets  of  celluloid  super- 
imposed upon  the  map  one  by  one  as  quickly  as  any  executive  com- 
mittee or  board  considering  the  proposals  may  desire.  The  main 
difficulty  with  the  celluloid  method  is  that  the  inks  will  rub  off  if  the 
celluloid  is  handled  too  much  with  moist  hands.  Ease  of  erasure  has 
some  advantages,  however,  for  tentative  schemes  can  be  rubbed  out 
or  changed  at  will,  simply  by  using  a  damp  cloth.  After  the  final 
adoption  of  the  plan,  tracing  cloth  can  be  laid  over  the  combined  map 
and  celluloid  sheet,  and  the  important  features  of  both  may  be  traced 
for  blue-printing  or  for  general  reference  later.  Where  maps  must  have 
constant  use,  it  is  sometimes  convenient  to  have  them  mounted  be- 
tween two  sheets  of  clear  celluloid.  The  celluloid-manufacturing  com- 
panies are  prepared  to  do  this  kind  of  mounting  to  order. 

Contrasts  in  map  areas  as  shown  in  Fig.  170,  by  superimposing 
one  portion  of  the  world  on  top  of  another  portion,  or  by  placing  two 
portions  side  by  side  on  the  same  scale,  are  of  considerable  value. 


MAP    PRESENTATIONS 


211 


In  geography  books,  and  in  other  places  where  maps  are  most  com- 
monly seen,  contrasted  territories  are  frequently  drawn  to  such  dif- 
ferent scales  that  a  true  idea  of  their  proportions  cannot  be  obtained. 
The  relative  proportion  can  be  indicated  best  when  care  is  taken  to 
have  the  several  areas  drawn  to  the  same  scale  and  placed  in  a  good 
position  for  comparison. 

Fig.  171  is  shown  here  only  as  an  example  of  the  almost  unlimited 
range  which  the  application  of  graphic  methods  may  have.  The  av- 
erage person  would  never  think  of  charting  a  football  game,  yet  the 
graphic  method  certainly  gives  the  information  more  concisely  than 
could  words  alone. 

Fig.  172  will  be  recognized  by  many  readers  as  similar  in  general 
scheme  to  the  weather  maps  on  which  lines  are  drawn  through  all 
points  having  the  same  temperature  or  the  same  barometric  pressure. 
Contour  lines  to  show  those  points  which  are  at  the  same  height 
above  sea  level  give  another  application  of  the  same  general  method. 
Profile  drawings  similar  to  Fig.  173  are  commonly  used  by  engi- 
neers, but  are  not  as  well  understood  as  they  should  be  by  others. 
The  main  feature  of  the  profile  chart  is  the  very  great  difference  be- 
tween the  horizontal  scale  used  to 
mark  distance  and  the  vertical 
scale  showing  the  height  of  the 
points  represented.  The  vertical 
scale  of  Fig.  173  should  have  been 
shown  on  the  chart.  The  heights 
stated  for  different  cities  give  a 
fair  indication  of  what  the  vertical 
scale  is  and  a  reader  can,  if  he 
must,  measure  on  the  drawing  the 
height  for  any  city  and  from  that 
determine  to  what  scale  the  draw- 
ing has  been  made.  As  a  broad 
rule,  the  scale  should  be  indicated 
in  an  easily  seen  position  on  every 
chart,  if  the  scale  can  be  of  assist- 

Warld's  Work  ,  i         •  i  .  i  ^ 

T?:^  ,-^     Tu    rt  xi      o-       i:  xt-       ance  to  any  one  besides  the  maker 

Fig.  170.    The  Comparative  Size  of  the        „    .        .    "^ 

Philippines  oi  the  chart. 

By  drawing  the  islands  to  scale  and  in  solid  black  Considerable  time  and  iugCnU- 

on  a  map  of  the  eastern  part  of  the  United       .  ,  i    •         i  • 

States,  the  relative  size  is  clearly  brought  out  ity  may   be  USed  in  drawing   Up   a 


212 


GRAPHIC    METHODS 


CO/7Z  S  ■  JO   •  /S  ■  20    SS     JO    JS-  -90     ^Sct^rtK  Its--  <iO  -JS  ■  JQ  ■  2S  ■  ZO  ■  JS     JO  ■  S-  COffZ 


Boston  Globe 


Fig.  171.     Second  Half  of  the  Harvard- Yale  Football  Game,  November  23,  1912, 

Final  Score,  Harvard  20,  Yale  o 

The  scale  of  the  football  field  has  been  changed  so  as  to  give  sufficient  width  for  representing  the  plays  by 

lines  and  symbols  of  various  kinds 


MAP    PRESENTATIONS 


213 


chart  like  Fig.  174  so  that 
the  facts  which  it  is  desired 
to  prove  may  be  brought 
out  clearly .  Numerous 
methods  are  available  for 
presenting  such  data. 
There  is  no  general  rule  for 
determining  which  method 
is  the  best,  and  judgment 
must  be  used  to  choose  the 
method  which  is  best  fitted 
to  each  individual  case. 
Note  that  in  Fig.  174  we 
have  a  scale  reading  to 
quarters  of  a  mile,  and  we 
also  have  circles  promi- 
nently drawn  on  the  map 
at  one-mile  intervals  to  give 
a  clear  idea  of  the  distances 
involved. 

Though  an  illustration  in  the  general  method  of  Fig.  175  is  at- 
tractive, and  will  effectively  gain  the  attention  of  the  reader,  the 
method  itself  has  all  the  inherent  weakness  of  Fig.  36,  Fig.  37  and  Fig. 
38  in  Chapter  III.  If  the  reader  wishes  to  practice  some  mental 
gymnastics,  he  may  try  to  work  out  the  ratio  between  the  number 
of  cattle  in  Idaho  and  the  number  of  cattle  in  Texas.  Though  it 
cannot  be  made  certain,  it  is  probable  that  the  chart  was  drawn  on 


Fig. 


Country  Gentleman 

172.  Dates  for  Planting  Com,  Showing  How 
the  Season  Advances  in  Different  Parts  of 
the  United  States 

This  illustration  is  similar  to  the  well-known  weather  maps  on 
which  lines  are  drawn  through  all  points  where  conditions 
are  the  same 


Railroad  Operating  Costs,  Suffern  &  Son,  New  York 


Fig.  173.  Profile  of  the  Pennsylvania  Railroad  from  Jersey  City  to  Chicago.  The 
Tabulated  Figures  Below  the  Profile  Refer  to  the  Spaces  Between  the  Dotted 
Lines 

This  is  an  example  of  a  valuable  method  of  presentation  by  which  a  horizontal  scale  much  smaller  than  the 
vertical  scale  is  used  so  that  great  distances  may  be  represented  in  a  small  space 


214 


GRAPHIC   METHODS 


an  area  basis.     For  the  purpose  of  a  visual  and  mental  test,  the  area 
basis  may  be  used  if  Idaho  and  Texas  are  compared. 

The  method  of  Fig.  176  is  now  quite  commonly  used  in  Govern- 
ment publications.  This  scheme  for  presenting  data  is  not  so  striking 
to  the  eye  as  that  of  Fig.  175,  but  it  is  more  accurate.  The  scale  given 
with  the  map  permits  the  number  of  cattle  for  any  State  to  be  read 
fairly  accurately.  The  degree  of  accuracy  depends  upon  the  map 
size  selected,  and  upon  the  number  of  dots  used  to  represent  any  given 
quantity.  The  more  dots  used  the  greater  the  accuracy.  There  is, 
r" 


Graham  Romeyn  Taylor  on  "Satellite  Cities"  in  the  Survey 


Fig.  174.  Map  Showing  that  Factory  Workers  of  Norwood  and 
Oakley  (Cmcinnati)  Live  Long  Distances  from  Their  Work, 
Many  in  the  Heart  of  Cincinnati  Rather  than  in  the  Sub- 
urbs Near  the  Factories 

The  use  of  much  heavier  lines  on  the  small  circles  and  the  figures  in  them  would 
have  improved  this  chart.  Pins  or  black-ink  dots,  each  representing  say  20 
workers,  would  give  a  good  result  by  using  the  method  of  Fig.  198 

however,  a  limit  to  the  number  of  dots  which  may  be  used,  or  the  dots 
will  of  necessity  be  so  small  in  diameter  that  the  quarter  circles  will 
be  impossible  for  the  eye  to  distinguish.  In  Fig.  176  it  would  not 
be  feasible  to  use  a  much  smaller  circle  if  the  quarter-circles  are  used. 


MAP    PRESENTATIONS 


215 


CountTv  Gentleman 

Fig.  175.    Relative  Distribution  in  the  United  States  of  Cattle  Other  than  Dairy  Cows 

For  popular  presentation,  if  great  accuracy  is  unimportant,  this  method  of  illustration  would  be  difficult  to 
improve  upon.  It  is  not  possible  to  get  a  correct  comparison  between  any  two  States  because  any  one 
circle  cannot  be  fitted  visually  into  the  area  of  another  circle.     Compare  the  method  used  in  Fig.  176 

f^f 


•  £00,000  cattle 

O  160,000  to  200,000  cattle 

O  100,000  to  150,000  cattle 

O  eO.OOO  to  100,000  cattle. 

O  Leas  tbaa  (0,000  cattle. 

The  heavy  lines  («■)  show  geographtc  divisions. 

Abstract  of  the  Thirteenth  Censtis  of  the  Untied  States,  1910 

Fig.  176.    All  Cattle  on  Farms  in  the  United  States,  by  States,  April  15,  1910 

Here  a  definite  scale  is  given  which  permits  fairly  accurate  reading  of  the  number  of  cattle  for  any  State. 
The  visual  contrast  between  States  is  also  quite  striking.  Though  not  so  clear-cut  as  Fig.  175,  this 
illustration  has  more  accuracy 


216 


GRAPHIC   METHODS 


In  making  up  copy  for  the  line  cut  of  Fig.  177  very  little  hand  work 
was  required.  If  an  outline  map  of  suitable  size  is  available,  the  only 
hand  work  necessary  for  a  cut  of  this  kind  is  in  drawing  the  small 
circles  and  placing  inside  them  the  figures  serving  as  key  numbers 
for  the  shading  used.  The  actual  shading  is  done  by  the  engraver 
making  use  of  the  Ben  Day  process.  For  information  regarding  the 
preparation  of  engraver's  copy  for  plates  on  which  Ben  Day  shading 
is  desired,  see  Fig.  233. 


HORSE 
7,000,000    — 

POWER      ^ 
9,000,000 

4,000,000    — 

7,000,000 

2,000,000    — 

4,000,000 

t.OOO.OOO    — 

2,000,000 

500,000    - 

1.000,000 

E50.000    - 

500,000 

100,000    — 

250,000 

50.000    - 

lOO.OOO 

LESS  THAN 

I5,000 

Fig.  1 77.    Potential  Water  Power  in  the  Different  States  of  the  United  States 

This  is  a  splendid  example  of  the  contrasts  in  shading  made  possible  by  the  Ben  Day  mechanical  processes 
of  engraving.  Nine  contrasting  shades  increasing  in  darkness  are  used  here  with  absolute  distinctness. 
The  small  number  in  the  circle  used  to  identify  the  shading  is  of  great  advantage 

There  is  one  serious  error  which  should  be  avoided  in  the  inter- 
pretation of  any  shaded  map  like  Fig.  177.  The  key  scale  at  the 
lower  left-hand  corner  of  the  illustration  shows  that  the  different 
shades  do  not  become  darker  by  any  uniform  increase  in  horse  power. 
The  range  included  in  shade  number  eight  is  50,000 — from  50,000 
to  100,000.  For  shading  number  two,  however,  the  range  is  3,000,000 — 
from  4,000,000  to  7,000,000.  This  numerical  scale  was  badly  selected, 
for  the  steps  vary  so  greatly  in  size  that  the  increasing  degrees  of  shad- 


MAP    PRESENTATIONS 


217 


rrm     Less  than    eo  bushels    per  acre. 

M2      20   -bo  40 

-40   bushels    per   acre,   aad  over. 


Fig.  178.    Yield  of  Com  per  Acre  in  the  Eastern  Part  of  the  United  States  in  1900 

Here  the  data  have  been  recorded  by  counties  rather  than  by  States.  This  chart  is  an  example  of  what 
any  draftsman  may  do  by  hand  shading.  It  would  have  been  better  to  use  the  smaller  numbers  to  rep- 
resent the  best  rank,  as  was  done  in  Fig.  177 


218 


GRAPHIC    METHODS 


MAP    PRESENTATIONS  219 

ing,  as  they  appear  to  the  eye,  mean  practically  nothing.  States  having 
shading  number  two  could  vary  from  each  other  in  the  amount  of 
horse  power  by  more  than  the  whole  quantity  of  power  in  States 
having  shadings  from  three  to  nine  inclusive.  If  the  steps  in  the 
shading  scale  had  been  so  made  that  there  were  nine  increasing  classes 
of  shading,  each  representing  1,000,000  horse  power,  it  can  be  seen 
that  all  the  States  here  numbered  five  to  nine  inclusively  would  have 
the  same  shading.  Such  a  map  made  with  a  scale  of  uniform  steps 
w^ould  appear  so  entirely  different  from  the  map  shown  here  that  no 
one  would  ever  recognize  the  maps  to  have  been  made  from  the  same 
data.  The  selection  of  scale  for  maps  of  this  kind  is  important  in  order 
that  the  map  may  tell  a  truthful  story.  Wherever  feasible,  the  nu- 
merical scale  intervals  for  colorings  or  shadings  should  be  uniform. 
Frequently  the  data  are  of  such  kind  that  there  is  much  concen- 
tration at  some  portion  of  the  scale,  but  with  important  facts  to  show 
at  other  portions  of  the  scale  above  and  below  the  point  of  greatest 
concentration.  It  may  then  be  desirable  to  use  uniform  scale-steps 
for  the  shading  in  the  portion  of  the  scale  with  greatest  concentra- 
tion, and  to  have  smaller  scale-steps  at  either  end  or  at  both  ends  of 
the  scale.  In  Fig.  177  small  scale-steps  would  seem  desirable  for  the 
lower  portion  of  the  scale. 

It  will  be  noticed  in  Fig.  177  that  the  numbers  denoting  the  shadings 
are  arranged  with  the  smallest  numbers  to  represent  the  largest  quanti- 
ties. This  arrangement  was  made  purposely.  On  a  map  of  the  kind 
seen  in  Fig.  177  there  may  be  any  number  of  different  shadings,  from 
one  to  a  dozen  or  more.  In  order  to  simplify  matters  for  the  reader  it 
seems  best  to  assign  the  smaller  numbers  to  represent  those  conditions 
which  are  considered  most  desirable  or  commendable.  The  reader  may 
then  see  instantly  which  areas  are  first,  second,  third,  etc.,  in  rank 
simply  by  observing  the  figures  inside  the  small  circles. 

In  Fig.  178,  if  it  be  assumed  that  there  is  a  likelihood  of  corn  crops 
going  up  to  60  bushels  per  acre,  the  scale  intervals  are  shown  as  uniform. 
Fig.  178  is  of  interest  chiefly  because  it  shows  what  can  be  done  by  hand 
ruling  when  it  is  necessary  to  produce  an  illustration  for  a  report  in 
w^iich  an  expensive  cut  by  the  Ben  Day  method  cannot  be  justified. 

Fig.  179  does  not  do  justice  to  the  possibilities  of  the  Ben  Day 
method  of  shading.  The  cut  was  made  by  photographing  a  page  of  the 
Census  Abstract  which  was  printed  on  rather  rough  paper.  With  an 
original  cut  made  directly  by  the  Ben  Day  process  the  distinctioii 


220 


GRAPHIC    METHODS 


between  the  different  shades  would  be  considerably  clearer  than  it  is 
in  Fig.  179.  A  cut  of  this  size  and  complexity  is  rather  expensive 
when  the  Ben  Day  shading  is  used.  Anyone  wishing  a  cut  made  with 
Ben  Day  work  would  do  well  to  get  a  rough  cost-estimate  from  his 
engraver  before  actually  giving  the  order. 

It  will  be  noticed  in  Fig.  179  that  the  numerical  scale-steps  for 
different  degrees  of  shading  are  uniform  except  at  the  smaller  end  of 
the  scale.  It  would  probably  not  be  wise  to  show  as  white  area  all 
of  the  land  valued  at  from  $10  to  $25  an  acre,  since  such  land  makes 


W  \      ■  ICHAMPsSiilT: 

It  MUPHWC\  V  ^ 


POnU  DAllPHINC 


itK.uoue 

r 


luiNtlll       ^KOUl 


g    >'  LAMSI 


k 


Berlillon's  "Course  elcmentalre  de  Statistique  Administrative" 

Fig.  i8o.    Height  of  the  Houses  m  the  Different  Districts  of  Paris 

The  scale  for  this  illustration  should  have  been  indicated  on  the  chart  so  that  actual  numbers  of  houses 
could  be  read.  The  vertical  dimension  of  the  group  of  bars  for  each  district  shows  the  relative  total  num- 
ber of  houses.     The  horizontal  dimension  shows  the  relative  number  of  houses  of  each  height  by  stories 

up  about  half  of  the  whole  United  States.  A  uniform  scale  varying 
by  $25  per  acre  would  give  an  erroneous  impression  regarding  those 
important  areas  which  contain  land  valued  at  less  than  $25  per  acre 
but  in  which  there  is  a  large  amount  of  farming. 

Map  diagrams  of  the  type  shown  in  Fig.  180  are  sometimes  useful. 
There  is  danger,  however,  of  making  a  chart  of  this  kind  so  popular 
in  character  that  it  loses  in  accuracy.     The  utility  of  Fig.  180  is  at  once 


MAP    PRESENTATIONS 

Population    Density  per  Acre. 


221 


. 

• 

a 

@ 

® 

a 

• 

• 

e 

® 

a 

e 

• 

• 

® 

(=) 

e 

© 

• 

• 

@ 

@ 

e 

0 

• 

•             • 

e 

e 
e 

0 
0 

0-50 


50-75 


75-100 


100 -1 50 


J  50 -EGO        200-E50 


250-300        3O0-350         350-400 


400-450        Over  450 

Courtesy  of  Graham  Romeyn  Taylor 


Fig.  i8i.    Methods  of  Marking  Maps  When  an  Increased  Density  of  Population 
May  be  Expected  in  Following  Years 

Each  shading  can  be  made  by  adding  with  a  pen  to  the  shading  used  for  the  next  lower  density.  Pins  of 
different  colors  placed  in  a  map  have  an  advantage  over  this  scheme  in  that  pins  can  be  removed  if 
population  density  should  happen  to  decrease 

limited  by  the  fact  that  there  is  no  key  scale  shown  from  which  an 
exact  numerical  interpretation  may  be  obtained. 

The  scheme  for  indicating  population  density  shown  in  Fig.  181 
is  necessary  only  when  very  large  and  valuable  maps  are  used.  For 
ordinary  purposes  it  would  be  better  to  have  a  new  map  for  each  Census, 
and  then  to  use  colored  crayons  on  the  different  areas  of  the  map, 
rather  than  to  attempt  the  complicated  scheme  of  Fig.  181.  If,  how- 
ever, a  photograph  must  be  taken  periodically  to  produce  line  cuts 
showing  the  map  in  printed  form  on  a  reduced  scale,  colored  crayons 
cannot  be  used  and  the  scheme  of  Fig.  181  may  be  of  great  assistance. 
The  result  obtained  by  the  method  of  Fig.  181  may  be  obtained  by  using 
map  pins  with  spherical  heads  and  pushing  the  pins  in  until  the  heads 
touch  the  map.  The  number  of  pins  in  any  city  block  or  district  would 
indicate  the  population  according  to  some  simple  scale.  If  it  is  not 
necessary  to  photograph  the  map,  pins  with  different  colors  of  heads 
may  be  used  to  show  density  of  population.  There  is  one  very  great 
advantage  in  using  pins  instead  of  crayons  or  the  pen-and-ink  system 
of  Fig.  181.  It  sometimes  happens  that  an  error  is  made  which  may 
spoil  a  very  valuable  map  because  of  the  impossibility  of  erasure.  When 
short  pins  are  used  instead  of  crayon  or  ink,  an  error  can  be  instantly 


222 


GRAPHIC    METHODS 


■I     I      I   NEW    ROADS  WHICH  EXHAUSTfO 
S>  50,000  000  BOND   ISSUE 
— —  ••—    ROAOS     BUILT    BEFORE    THE 
DIX   ADMINISTRATION 
>*••  ROADS  TO   BE   BUILT    UNDER   SECONff 
^£0,000,000    BOMD    ISSUE 


\'aff«-*"A 


.  !     />f UJ.T>01«  CMACM  ,  '^<,  III 

;;v,ECor^Nj;i^^         CREEK.  J     ,,  /f         P1.E*"       \      U— -•           \    '.  !) 

-A_  f^l^—^i      ""    *^Kb'*Lv'>\/         ,..._';-- .     \'.  _: Xl'*'W*    /I 


mjiilT''^'"^/^'"-'':^  k 


irw.  Pierrepont  White,  of  Uttca.  N.  Y.,  in  the  New  York  Tlmea 

Fig.  182.  Map  Showing  3,500  Miles  of  Completed  and  Proposed  State  Roads,  in 
New  York's  Proposed  12,000-Mile  System.  The  Shaded  Portion  Shows  a 
Strip  Ten  Miles  Wide  which  Contains  90  Per  Cent  of  the  Taxable  Valuation  and 
80  Per  Cent  of  the  Population 

The  object  of  the  illustration  is  to  show  the  necessity  of  a  road  system  that  will  feed  from  the  farms  to  the 
densely  settled  portion,  permit  the  quick  and  easy  transportation  of  farm  products  to  the  cities,  lessen 
the  cost  of  living,  and  thus  justify  the  taxing  of  the  State  as  a  whole  for  the  construction  of  this  system 

corrected  by  pulling  out  pins.  Also,  if  there  should  be  a  reduction  in 
the  density  of  the  population,  pins  can  be  pulled  out,  whereas  with  the 
pen-and-ink  method  of  Fig.  181  it  is  not  possible  to  proceed  backward 
on  the  scale  of  marking  and  a  decrease  can  never  be  shown  without 
making  another  map  or  marring  the  old  one. 

In  Fig.  182  is  seen  a  good  example  of  the  graphic  method  applied 
to  newspaper  writing  designed  to  convince  the  reader  by  specific 
argument.  The  presentation  is  very  effective.  The  shaded  portion 
of  the  map  shows  a  strip  which  contains  90  per  cent  of  the  taxable 
valuations  and  80  per  cent  of  the  population.  The  possibilities  for  the 
use  of  maps  in  arguments  of  political  or  economic  nature  are  almost 


MAP    PRESENTATIONS 


223 


without  limit.  It  is  rather  surprising  that  maps  for  such  purposes 
have  not  been  more  generally  employed. 

Though  the  map  record  sheet  shown  in  Fig.  183  may  appeal  to 
some  business  men,  there  would  seem  to  be  little  advantage  in  that  type 
of  sheet  over  tabulated  figures  in  a  column.  The  column  arrangement 
would  have  a  desirable  feature  in  that  different  entries  could  more 
easily  be  compared  for  size  by  judging  the  number  of  digits  contained 
in  each  entry. 

The  method  shown  in  Fig.  184  can  be  widely  used  in  map  problems 
relating  to  any  kind  of  travel  over  specific  routes.  In  this  particular 
case  the  map  concerns  the  movement  of  freight.  Maps  of  this  type 
are  very  commonly  used  to  show  the  number  of  passengers  carried  on 
different  city  transit  lines.  To  make  an  illustration  on  the  plan  of 
Fig.  184,  the  width  of  each  broad  strip  is  carefully  drawn  to  some  scale 
representing  the  total  quantity  movement.  A  map  like  this  is  easily 
drawn  yet  it  is  very  effective,  particularly  if  colors  are  used  for  the  broad 
strips  while  the  route  itself  is  marked  by  means  of  a  black  line  in  the 
center. 


SHIPMENTS  TO  CONS'     JIERS  AND  0EALCR9 
rORTHE ^ENDINQ     |g 


By  Permission  of  "System'' 


Fig.  183. 


Blank  for  Recording  Sales  to  Consumers  and  to  Dealers,  Abbreviated 
by  the  Letters  "C"  and  "D"  for  Each  State 

A  blank  like  this  can  be  filled  out  daily,  weekly,  or  monthly  as  desired 


224 


GRAPHIC   METHODS 


Maps  on  the  scheme  of  Fig.  184  are  made  entirely  in  the  plane  of 
the  paper  itself.  In  Fig.  185  we  have  a  map  presentation  in  which 
quantities  are  represented  by  building  vertically  above  the  various 
routes  laid  out  on  the  map.  For  the  map  of  Fig.  185,  the  vertical 
representation  was  made  by  strips  of  wood,  alternately  black  and  white, 
glued  carefully  above  each  one  of  the  street-car  routes.  Each  of  the 
strips  of  wood  represents  4,000  passengers  carried  on  the  street-car  lines 
in  24  hours.  The  model  gives  the  whole  transit  situation  with  sur- 
prisingly great  clearness,  and  a  better  presentation  than  this  could 
scarcely  be  imagined. 


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Railway  Age  Gazette 


Fig.  184.     Map  Diagram  Showing  Freight-traffic  Density  and  Direction  on  the  St. 
Louis  and  San  Francisco  Raihoad  for  the  Fiscal  Year  1912-13 

The  figures  are  in  terms  of  100,000  net  tons  hauled  one  mile  per  mile  of  road. 

A  map  of  this  kind  is  easily  made  and  is  often  of  very  great  utility.     The  method  can  also  be  used  to  show 
the  number  of  passengers  carried  on  railroad,  subway,  or  street-car  lines,  etc.     Compare  Fig.  185 

The  method  used  in  the  construction  of  the  model  shown  in  Fig.  185 
gives  magnificent  results,  but  wooden  strips  are  not  practicable  except 
on  a  very  spacious  map.  The  wood-strip  method  also  involves  a  large 
amount  of  time  on  the  part  of  a  skilled  workman,  and  workmen  to 


Courtesy  of  Dt.  Ewerbeck,  Internationale  Baufach-Amstelhmg,  Leipzig,  Germany,  191S 

Fig.  185.    Passengers  Carried  in  Twenty-four  Hours  on  the  Street-car  Lines  of 
Frankfurt  a  M.,  Germany.    Each  Vertical  Strip  Represents  4,000  Passengers 

The  map  is  about  eight  feet  square.     Strips  of  wood  are  glued  above  each  street  having  a  car  line.     This 

is  an  excellent  presentation  of  facts 

225 


226  GRAPHIC   METHODS 

do  this  class  of  work  are  not  so  easily  found  in  the  United  States  as 
in  Germany. 

An  excellent  map  of  this  general  type  can  be  made  by  using  sheet 
metal,  as  aluminum  or  zinc,  ruled  or  painted  with  lines  or  colored 
stripes  representing  the  vertical  scale  to  which  the  information  is  to  be 
shown.  Where  two  transit  lines  intersect  the  strips  of  metal  can  be 
riveted  or  soldered  together.  As  aluminum  is  not  easily  soldered  it  is 
best  to  use  zinc  or  tinned  iron  if  solder  is  to  be  the  means  of  holding  the 
vertical  strips  to  each  other.  In  many  cases  solder  is  unnecessary,  for 
the  strips  may  be  held  vertically  by  notching  each  strip  halfway  through 
so  that  the  strips  can  be  interlocked  in  the  manner  shown  in  Fig.  236. 
By  using  sheet  metal  a  much  cheaper  construction  can  be  obtained  than 
by  wood  strips.  The  sheet-metal  method  also  permits  the  use  of  a 
map  of  much  smaller  size  and  finer  scale  than  would  be  feasible  if  wood 
strips   were  the  means   of  obtaining  the  necessary   vertical  height. 


Chapter  XII 
MAPS  AND  PINS 

PIN  MAPS  have  not  been  much  used  in  the  past,  chiefly  because 
a  map  pin  which  would  give  satisfactory  service  has  not  been 
available  for  common  use.  Until  recently  the  map  markers 
obtainable  have  been  little  more  than  old-fashioned  carpet  tacks  having 
chisel-shaped  points  which  cut  the  surface  of  any  map  into  which  they 
were  pushed.  Tacks  with  rough  steel  shanks  cannot  be  pushed  far 
into  a  map  if  the  tacks  are  to  be  pulled  out  again.  Also,  rough  steel  is 
likely  to  rust  so  as  to  cause  the  whole  tack  to  deteriorate  rapidly. 

Cloth  heads  on  the  map  tacks  make  it  possible  to  have  tacks  in  dis- 
tinct colors  and  plaids.  The  cloth  tops,  however,  fade  in  the  sunhght 
and  collect  dust  so  that  in  a  short  time  the  different  colors  of  tacks  on 
any  map,  exposed  as  a  wall  map  must  be,  cannot  be  easily  distinguished. 
The  crudeness  of  the  cloth-covered  tack  makes  it  unsatisfactory  for 
many  kinds  of  map  work.  Cloth-covered  tacks  are  long,  and  long  tacks 
which  can  be  pushed  only  a  short  distance  into  the  surface  of  a  map  are 
not  satisfactory,  for  they  are  likely  to  drop  out  or  be  knocked  off  by 
any  slight  disturbance. 

Wall  maps  with  long  projecting  tacks  are  not  practical  for  office 
use  unless  protected  by  an  expensive  frame  with  a  glass  cover.  As  it 
is  usually  necessary  to  open  up  such  a  glass  map-case  to  change  the 
position  of  the  tacks  frequently,  the  construction  of  the  case  becomes 
unduly  expensive.  Without  a  glass  cover  a  wall  map  with  long  pro- 
jecting tacks  is  likely  to  be  damaged  by  the  feather  duster  of  the  janitor. 

Even  when  maps  with  long  projecting  tacks  are  safeguarded  by 
being  placed  in  separate  drawers  of  a  cabinet  made  for  that  purpose, 
there  is  still  a  probability  that  some  of  the  tacks  will  come  loose  from 
the  mounting  and  rattle  around  inside  of  the  map  drawers.  This  is 
a  point  not  realized  by  most  men  who  install  map  and  tack  systems, 
but  it  usually  sooner  or  later  sounds  the  death -knell  of  the  tack  system. 

227 


t 


228  GRAPHIC    METHODS 

Generally  the  tacks  are  placed  in  the  maps  one  by  one  as  agencies  are 
established  or  as  data  are  obtained  from  correspondence.  After  the 
correspondence  by  which  each  tack  was  located  has  gone  to  the  cor- 
respondence files,  there  is  ordinarily  no  list  showing  the  geographical 
location  of  the  tacks.     If  a  single  tack  is  found  loose  in  the  bottom  of 

a  drawer  of  a  cabinet  system,  or  on 
the  floor  of  an  office  where  there  is  a 
wall  map,  it  causes  distrust  of  the 
whole  tack  installation.  When 
there  is  no  list  showing  the  geo- 
graphical location  of  different 
Fig.  i86.    A    Contrast    Between    Long,     tacks,     the    one    tack    which    is 

LS;rr:flo:{;I:rGtss-he"d  -^  °f  Pl-^  --»*  ^e  put  back 
Map  Pins  Made  with  Short  Needle-  without  checking  over  corre- 
pointssothatthePinsMaybe Pushed  spondence  and  records  which 
in  until  the  Heads  Touch  the  Map  .       ^  i      ^    p  t-» 

may  extend  back  tor  years.     Jbven 

when  a  list  of  tack  locations  is  at  hand,  the  loose  tack  cannot  be  replaced 
without  checking  the  location  of  all  the  tacks  on  the  map  one  by  one 
to  determine  by  a  process  of  elimination  where  the  loose  tack  came  from. 
In  the  ordinary  course  of  human  events  it  is  not  likely  that  a  tack  falling 
out  of  a  map  would  be  found  to  give  warning  that  the  map  record  is 
no  longer  accurate.  The  tack  system  using  long  projecting  tacks  may 
therefore  contain  unsuspected  inaccuracies  just  because  tacks  may  have 
come  loose.  The  unpleasant  suspicion  that  a  map  record  may  be  inac- 
curate, because  of  the  long  tacks  falling  out,  sometimes  causes  a  man  to 
abandon  the  tack  system  entirely,  believing  that  it  is  not  reliable 
enough  to  give  data  on  which  important  decisions  must  be  based. 

Map  and  pin  systems  are  of  such  tremendous  assistance  that  they 
should  not  be  condemned  simply  because  the  map  pin  itself  has  not 
been  satisfactory.  By  using  a  short  pin  with  a  needle  point  and  by 
having  a  backing  for  the  map  such  that  the  needle  point  can  be  pushed 
in  until  the  spherical  head  touches  the  map,  we  can  secure  a  map 
system  which  is  absolutely  trustworthy.  Since  the  pin  is  pushed  in  to 
its  full  length,  a  blow  cannot  dislodge  it.  The  spherical  head  in  contact 
with  the  map  gives  a  very  neat  appearance,  yet  the  spherical  shape  per- 
mits the  fingers  to  remove  the  pin  by  straight  pulling  without  any  diffi-l 
culty  whatever.  The  smooth  needle-point  of  good  quality  steel  does  not 
rust  easily  and  it  does  not  cut  the  surface  of  the  map.  When  a  pin| 
must  be  removed,  the  hole  is  so  small  that  it  is  scarcely  noticeable. 


MAPS    AND    PINS  229 

Pins  having  spherical  glass  heads  may  be  used  on  wall  maps  with- 
out any  danger  of  the  heads  fading  from  sunlight.  The  glass  surface 
is  so  smooth  that  dust  cannot  collect  sufficiently  to  affect  the  color 
appearance  of  the  pin  head.  Even  if  the  map  does  get  dusty,  it  is 
perfectly  safe  to  use  the  feather  duster  on  a  wall  map  having  pins  which 
are  pushed  in  so  far  that  the  spherical  heads  are  in  contact  with  the 
map  surface.     Dusting  of  such  a  map  will  not  loosen  the  pins  in  any 


^fe3^^;;;Mi4^:/ J         '.:.,,  :W^ 


me- 


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'i  \     ■         tV-:     -   \^  ..^R, 


Revieic  of  Reviews 

Fig.  187.  Location  of  the  Plants  Affiliated  with  the  University  of  Cincinnati,  College 
of  Engineering.  Every  Star  Represents  a  Plant  Where  Co-operative  Engineer- 
ing Students  are  Employed 

A  wall  exhibit  like  this  is  easily  made  by  using  a  red  legal  seal  and  red  stars  such  as  can  be  purchased  at 

many  good  stationery  stores 

way.  A  wall  map  on  which  pins  with  spherical  glass  heads  are  used  can 
be  very  cheaply  mounted,  it  needs  no  glass  cover,  and  the  pins  can  be 
put  in  or  taken  out  instantly,  thus  giving  a  location  record  which  is  at 
all  times  in  plain  view,  yet  thoroughly  accurate. 

Another  great  advantage  of  the  pins  with  spherical  glass  heads  is 
that  they  may  be  obtained  with  small-diameter  heads,  which  permit 
the  use  of  numerous  pins  on  maps  of  small  size.     In  portraying  many 


230  GRAPHIC    METHODS 

classes  of  information,  it  is  impracticable  to  use  the  cloth-head  tacks 
because  the  heads  are  so  large  that  the  tacks  touch  each  other  in  all 
thickly  populated  regions. 

Photographs  taken  of  a  map  containing  tall  pins  or  tacks  give  an 
inaccurate  effect,  since  the  angle  of  the  lens  causes  the  head  of  the 
tack  to  appear  at  one  side  of  the  point  in  which  the  tack  itself  is  lo- 
cated. Thus,  in  a  photograph  of  a  map  of  the  United  States  the  head 
of  a  long  pin  or  tack  set  at  Providence,  R.  I.,  might  well  show"  near 
Boston,  Mass.  There  is  no  way  of  avoiding  this  error  if  projecting 
pins  and  tacks  are  used.  The  only  safe  plan  is  to  use  the  spherical  pin 
head  which  is  in  contact  with  the  map  surface  itself.  Photographic 
views  of  a  sphere  are  the  same  from  all  directions,  thus  causing  all 
pins  to  appear  exactly  the  same  size  and  shape  on  the  photograph. 
Photographs  taken  of  a  large  map  with  flat-headed  tacks  show  the 
heads  in  the  center  of  the  picture  as  circles,  while  the  heads  towards 
the  edge  of  the  picture  look  of  much  smaller  size,  because  they  appear 
flattened  out  as  ellipses.  The  visual  effect  for  points  toward  the  edge 
of  the  map  is  lessened  when  the  tacks  are  flat  headed,  and  an  un- 
necessary visual  error  is  brought  into  the  picture. 

A  very  cheap  yet  satisfactory  mounting  for  a  wall  map  to  be  used 
with  glass-head  map  pins  is  made  with  three  or  more  layers  of  corru- 
gated straw-board.  The  straw-board  used  should  be  about  7i6-inch 
thick  with  a  facing  on  either  side  of  the  corrugated  portion.  Three 
thicknesses  of  straw-board  are  suflScient  to  give  strength  for  any  map 
up  to  one  yard  long.  The  two  outside  layers  of  straw-board  should 
be  so  arranged  that  the  corrugations  will  run  with  the  length  of  the 
map,  thus  giving  the  greater  strength  in  that  direction.  The  middle 
layer  should  have  the  ribs  running  crosswise  of  the  map  so  that  the 
map  mounting  will  be  safeguarded  from  bending  in  either  of  the  two 
different  directions.  Where  very  large  wall  maps  are  desired,  six  or 
more  layers  of  straw-board  may  be  used  to  give  suflScient  strength.  If 
single  sheets  of  straw-board  cannot  be  found  as  large  as  the  map 
itself,  the  map  mounting  can  easily  be  built  up  of  small  sheets  of 
straw-board,  provided  the  joints  in  the  straw-board  are  so  placed 
that  they  will  not  be  over  each  other  to  weaken  the  finished  structure. 

The  straw-board  backing  for  a  map  to  be  used  with  pins  is  not 
the  best  obtainable  if  the  pins  must  be  put  in  and  taken  out  frequently. 
When,  however,  the  pins  are  to  be  placed  in  the  map  and  left  there, 
the  straw-board  is  just  as  satisfactory  as  any  other  backing  for  a 


MAPS   AND    PINS  231 

map.  A  layer  of  the  cheapest  kind  of  muslin  placed  over  the  face  of 
the  straw-board  will  prevent  the  pins  from  tearing  the  surface  of  the 
map  if  they  happen  not  to  be  pushed  in  exactly  straight.  The  use  of 
cloth  over  the  straw-board  also  permits  of  changing  the  pins  many  more 
times  than  would  be  feasible  with  straw-board  without  the  cloth 
reinforcing. 


.  •  *'.''  '• 


"'  '    '^."'"^ 


Heoiew  of  Reviews 

Fig.  i88.    Every  Pin  Dot  on  this  Map  Marks  the  Home  of  a  Student  of  the  University 

of  Cincinnati 

By  using  a  map  printed  in  colors  which  do  not  photograph  as  black,  the  pins  show  up  distinctly  on  the  map 

as  a  background 

Before  mounting  a  map  the  colors  should  be  tested  to  make  sure 
that  they  will  not  run  in  water.  The  map  should  then  be  wet  all 
over,  preferably  by  laying  it  flat  for  a  time  in  a  large  tray.  Use  a 
flour-and-water  starch  paste,  paper-hanger's  paste,  or  library  paste 
of  the  kind  used  in  mounting  photographic  prints.     Carefully  remove 


232 


GRAPHIC    METHODS 


all  wrinkles  and  press  the  excess  paste  out  from  under  the  edge  of 
the  map.  Shrinkage  of  the  map  and  of  the  moistened  straw-board 
surface  will  almost  certainly  cause  the  straw-board  mounting  to  warp 
unless  care  is  taken  to  prevent  warping.  At  the  same  time  the  map 
is  pasted  on  the  front  of  the  straw-board,  paste  a  sheet  of  wet  wrapping 
paper  on  the  back  of  the  straw-board  mount.  The  shrinkage  of  the 
wrapping  paper  on  the  back  will  equalize  the  shrinkage  of  the  map 
on  the  front  of  the  mount.  Place  the  mounted  map  on  a  flat  table 
surface  or  on  a  smooth  floor,  and  stack  books  or  other  heavy  articles 
upon  the  mount  over  night  or  until  thoroughly  dry  so  that  any  ten- 
dency to  warp  in  the  drying  may  be  overcome  by  the  weights. 

Finish  the  four  edges  of  the  corrugated  straw-board  by  using 
gummed  cloth  tape  or  paper  tape  neatly  folded  over  the  edges  in  the 
manner  ordinarily  used  with  passe-partout  pictures.    To  hang  up  the 

finished  map  use  two  com- 


c»/i/}r  /Noic/ir//vG  o/srf>/si/r/of\/  or  thc  r/ci.D  sc/}v/cc 


bination  clamps  and  rings 
such  as  may  sometimes  be 
obtained  in  stores  selling 
window  shades.  These 
metal-clamp  fixtures  are  of 
neat  appearance  and  of 
strength  sufficient  to  hold 
a  map  of  any  size.  If  two 
nails  or  hooks  are  used  in 
the  wall  to  support  the 
map,  the  ring  hangers  allow 
the  map  to  be  instantly  re- 
moved to  a  desk  when  addi- 
tional pins  must  be  put  in. 
If  pins  are  to  be  put  in  and  taken  out  of  a  map  repeatedly,  it 
should  be  mounted  on  good  quality  cork  composition.  Exhibition- 
board,  compo-board,  wall-board,  or  any  of  the  various  boards  gener- 
ally used  for  wall  surfaces  may  be  used  as  a  backing  to  give  strength 
to  the  cork.  Care  should  be  taken  to  get  a  good  quality  of  board 
which  will  not  warp  seriously.  The  cork  composition  can  be  glued 
to  the  wall-board  and  then  the  map  pasted  on  the  cork.  A  piece 
of  wrapping  paper  should  be  pasted  on  the  back  of  the  wall-board 
at  the  time  the  map  is  mounted  so  that  the  shrinkage  of  the  map 
may  be  equalized.     The  edge  of  the  cork  mounting  may  be  bound 


Counlru  Utntleman 

Fig.  189.  Distribution  of  the  Field  Service  of 
the  Department  of  Agriculture,  February  i, 
1912 

A  pin  map  cannot  be  excelled  for  conveying  information  like 
this.  Note  the  great  activity  of  the  Agricultural  Depart- 
ment in  the  South 


MAPS    AND    PINS 


233 


T/iuiii(t.\  a.  Plant  A  Co.,  Queen  Qualily  Shoes 

Fig.  190.     The  Use  of  Pin  Maps  in  Advertising 

A  large  shoe  manufacturing  company  used  this  illustration  in  an  advertisement  announcing  that  3,800 

merchants  were  ready  to  show  the  latest  fall  and  winter  models  of  shoes 
In  order  to  make  the  dots  stand  out  distinctly  it  would  appear  that  agencies  in  any  State  have  been  shown 

as  imiformly  distributed  over  the  State.     Actual  exact  locations  would  be  almost  impossible  to  show 

unless  a  much  larger  map  were  used 

with  a  cloth  tape  as  suggested  for  straw-board  mounts,  or  the  whole 
built  up  combination  may  be  framed  with  picture  framing  but  without 
using  any  glass  covering.  The  cork  composition  used  should  be  Vs-inch 
thick.  Maps  backed  with  cork  composition  and  used  with  glass-head 
pins  having  needle  points  will  permit  almost  unlimited  puncturing 
from  frequentl}^  moved  pins.  If  the  map  is  mounted  on  cork  composition 
the  sharp-pointed  pins  are  easily  pushed  in  and  removed,  yet  the  record 
is  always  accurate  because  the  pins  cannot  be  knocked  out. 

Numerous  wall  maps  can  be  very  conveniently  used  if  they  are 
mounted  on  vertical  swinging-leaf  display  fixtures  similar  to  those 
shown  in  Fig.  219.  The  two  surfaces  of  each  swinging  leaf  should  be 
covered  with  corrugated  straw-board  and  muslin,  or  preferably  with 
cork  composition  in  order  to  get  a  good  surface  into  which  to  insert 
the  pins.  As  adjacent  leaves  are  likely  to  strike  and  break  the  glass 
heads  of  the  pins,  projecting  bumpers  should  be  placed  on  every 
other  leaf  to  allow  enough  clearance  for  opposite  pins  when  the  leaves 
come  in  contact.     The  rubber-covered  bumpers  used  to  prevent  door 


234  GRAPHIC    METHODS 

knobs  from  striking  plastered  walls  can  be  placed  at  the  top  or  bottom 
of  alternate  leaf  surfaces.  If  these  rubber  bumpers  are  not  available, 
a  narrow  strip  of  wood  at  the  top  and  bottom  of  each  leaf  will  serve. 

When  employed  with  glass-head  pins  having  needle  points,  the 
drawer  cabinets  for  maps  used  to  route  salesman,  etc.,  can  have  a 
layer  of  cork  composition  fastened  in  the  bottom  of  each  drawer. 
The  maps  are  then  glued  to  the  surface  of  the  cork  composition.  The 
drawer  cabinets  regularly  found  on  the  market  have  sufficient  drawer 
depth  to  permit  placing  a  J^-inch  layer  of  cork  composition  in  the 
bottom  of  each  of  the  regular  drawers  and  still  allow  room  for  the 
pins.  Map  pins  may  be  pushed  into  the  cork  composition  so  se- 
curely that  no  pin  will  ever  be  misplaced  even  if  a  book  or  other  heavy 
object  should  happen  to  drop  upon  the  map  and  the  map  pins.  Pins 
in  cork  composition  are  so  easily  inserted  and  removed  that  they  can 
be  handled  more  rapidly  than  if  stuck  into  any  kind  of  a  board  sur- 
face. When  ordering  maps  from  any  map  manufacturer  or  map  store 
for  use  with  glass-head  pins  care  must  be  taken  to  specify  either  a 
cork-composition  backing  or  a  corrugated  straw-board  backing,  else 
the  map  will  probably  be  shipped  mounted  on  compo-board  or  some 
other  surface  entirely  too  dense  to  permit  of  pushing  the  map  pins 
in  until  the  heads  touch  the  surface  of  the  map. 

If  numerous  glass-head  pins  are  to  be  put  into  a  map  at  one  time, 
the  eraser  in  the  end  of  a  lead-pencil  should  be  used  to  push  the  pins 
down  until  the  heads  touch  the  map.  Pins  can  be  very  quickly  lo- 
cated if  only  their  points  are  pushed  into  the  map  by  hand,  leaving 
the  main  pressure  to  be  applied  by  the  lead-pencil  eraser  after  a  num- 
ber of  pins  have  been  located.  The  pencil-eraser  method  saves  time 
and  it  also  eliminates  the  discomfort  which  may  be  caused  if  thousands 
of  pins  are  pushed  into  a  map  by  using  the  thumb  and  forefinger  only. 

Line  cuts,  sometimes  called  zinc  cuts,  may  be  made  directly  from 
pin  maps  if  glass-head  map  pins  of  suitable  color  are  used.  At  the 
point  on  the  map  where  each  pin  head  is  located  there  will  be  a  black 
dot  on  the  print  made  from  the  zinc  cut.  As  light  is  reflected  from 
the  surface  of  the  glass  heads  of  the  pins,  there  are  sometimes  shown 
in  a  photograph  high  lights  which  must  be  retouched  with  a  pen  or 
a  fine  brush  so  that  the  whole  spot  shall  be  black,  rather  than  black 
with  a  white  center,  as  seen  in  Fig.  191.  Anybody  can  do  this  re- 
touching very  quickly.  It  is  mentioned  here  only  as  a  caution  that 
the  photograph  be  inspected  before  the  zinc  engraving  is  made  from  it. 


MAPS   AND    PINS  235 

Photographs  for  line  cuts  must  have  a  good  contrast  of  white  and 
black,  or  colors  which  photograph  as  black.  Photographs  or  original 
drawings  containing  shades  of  gray  will  not  produce  good  line  cuts 
and  frequently  cannot  be  used  at  all  for  the  zinc  engraving  process. 
When  line  cuts  are  to  be  made  from  pin  maps  it  is  best  to  be  certain 
that  the  glass-head  pins  are  selected  in  colors  which  will  photograph 
as  black.  Red,  orange,  and  black  pins  can  be  used  without  any  ques- 
tion, since  negatives  made  from  these  colors  give  a  dead  black  on 
the  photographic  print.  Line  cuts  can  also  be  made  from  dark  green 
and  some  of  the  other  colors.  Where  it  is  necessary  to  make  photo- 
graphs and  line  cuts  from  a  very  expensive  and  elaborate  pin  map, 
it  is  wise  to  consult  the  engraver  before  the  pin  colors  for  the  map  are 
finally  decided  upon.  The  color  blue  should  be  carefully  avoided  if 
photographs  or  line  cuts  are  to  be  made,  since  blue  almost  totally  fails 
to  show  up  on  a  photograph. 

If  half-tone  engravings  can  be  used  to  illustrate  the  pin  map, 
many  more  different  colors  of  pins  may  be  used  on  the  original  map  than 
when  zinc  cuts  are  the  means  of  printing.  Another  advantage  of 
half-tones  is  that  different  colors  of  pin  heads  are  represented  in  the 
half-tone  by  different  shades  of  gray,  as  can  be  seen  in  Fig.  191.  On 
the  left  half  of  Fig.  191,  fourteen  different  colors  of  glass-head  map 
pins  were  used.  The  photograph  was  not  retouched  in  any  way. 
Fig.  191  thus  represents  about  what  can  be  expected  of  different 
colored  pin  heads  for  contrast  in  half-tone  illustration.  Note  the 
high  lights  which  give  white  spots  on  the  circles  of  the  darker  pin  heads. 
It  is  spots  like  these  which  should  be  retouched  by  hand  on  any  photo- 
graph from  which  a  line  cut  is  to  be  made. 

Tacks  and  pins  have  been  used  on  maps  to  locate  agencies,  sales- 
men, customers,  etc.,  more  than  for  any  other  one  purpose.  The 
various  possibilities  in  applying  tacks  and  pins  to  sales-department 
work  cannot  be  thoroughly  covered  here,  but  if  a  few  general  methods 
are  known,  each  sales  manager  can  work  out  for  himself  the  pin  scheme 
which  best  suits  his  own  conditions. 

Fig.  191  was  photographed,  without  any  retouching,  direct  from 
a  section  of  the  United  States  Geological  Survey  topographical  maps. 
These  contour  maps,  having  a  scale  of  about  one  inch  to  the  mile, 
may  be  obtained  from  the  Geological  Survey  at  Washington,  for  most 
of  these  sections  of  the  country  which  are  thickly  settled.  The  maps 
are  very  low  in  cost  and  yet  are  remarkably  accurate.    Fig.  191  was 


236 


GRAPHIC    METHODS 


^  u  o 


rf/       > 


MAPS    AND    PINS  237 

purposely  photographed  at  an  angle  of  about  45  degrees.  As  the 
upper  part  of  the  illustration  is  out  of  focus  because  of  the  angle, 
the  illustration  does  not  do  justice  to  the  Government  maps.  Another 
reason  why  the  map  does  not  come  out  clearly  is  that  brown  ink  is 
used  to  print  the  contour  lines  and  these  lines  accordingly  show  only 
faintly  in  the  half-tone. 

When  it  is  necessary  to  show  the  routing  to  various  points  on  a 
map  the  best  method  is  to  use  a  fine  red  string  or  thread  between 
map  pins  as  seen  in  Fig.  191.  If  the  routing  must  be  changed  the 
thread  can  be  almost  instantly  moved  to  connect  the  pins  in  some 
new  order.  Lines  could  be  drawn  on  a  map  in  ink  to  show  routing, 
but  the  map  would  be  ruined  if  any  change  in  routing  should  ever  be 
necessary. 

In  the  preparation  of  illustrations  for  reports,  advertising,  etc., 
whether  maps  with  or  without  pins  are  used,  great  care  must  be  taken 
in  the  selection  of  the  map  itself.  Map  manufacturers  have  a  very 
annoying  custom  of  purposely  making  maps  in  such  manner  that  the 
maps  cannot  easily  be  duplicated  by  photographic  processes.  Maps 
printed  in  blue  ink  are  almost  hopeless  for  use  in  making  zinc  cuts. 
Maps  on  which  large  areas  as  States,  or  counties,  are  differentiated  by 
the  use  of  colors  red,  orange,  green,  etc.,  do  not  produce  either  good 
line  cuts  or  good  half-tones  since  the  colored  areas  on  the  original  maps 
are  likely  to  show  as  solid  black  areas  and  blot  out  all  detail  on  the 
photograph.  If  an  illustration  must  be  made  from  a  map  it  is  well  to 
be  sure  that  the  map  is  printed  in  black,  red,  or  orange  outline  so  that 
the  resulting  photograph  will  have  distinct  contrast.  Maps  should 
contain  as  little  detail  as  practicable,  to  make  certain  that  the  pin  heads 
or  other  representations  of  specific  data  will  show  up  as  distinctly  as 
possible.  Fig.  192  is  a  good  example  of  the  kind  of  map  to  use  for 
reproduction  when  pins  are  employed.  Notice  in  Fig.  192  a  heavy 
border  for  the  country  as  a  whole,  and  the  outlines  for  each  State. 
Towns  and  rivers  are  not  shown.  Each  dot  on  the  map  may  thus  be 
seen  with  great  clearness. 

As  maps  are  very  carefully  copyrighted  by  most  map  publishers, 
maps  which  are  copyrighted  should  not  be  reproduced  without  con- 
sideration of  the  copyright.  For  maps  which  are  photographed  down 
with  comparatively  little  change,  permission  should  be  requested  from 
the  map  publisher,  to  make  certain  that  unpleasant  complications  such 
as  damage  suits  or  the  holding  up  of  a  publication  may  be  avoided. 


238 


GRAPHIC    METHODS 


The  228  Principal  Trading  Centers 


Saturday  Evening  Post,  Curtis  Publishing  Co. 

Fig.  192.    The  228  Principal  Trading  Centers  in  the  United  States 

This  illustration  was  taken  from  an  advertisement  proclaiming  that  a  certain  magazine's  circulation  was 
mainly  in  the  228  chief  trading  centers  of  the  country,  and  that,  accordingly,  the  magazine  must  be 
effective  as  an  advertising  medium  for  merchandise 

Note  that  in  the  east  the  dots  are  so  numerous  they  are  shown  as  crescents.  The  crescent  scheme  is  a  good 
one  as  it  permits  the  use  of  a  much  larger  dot  than  would  otherwise  be  possible 

The  amount  of  detail  which  may  be  permitted  on  any  map  in  which 
pins  are  used  depends  on  the  size  of  the  resulting  illustration  and  the 
size  of  the  pin  heads.  If  the  pins  are  so  numerous  that  the  map  must 
be  very  large,  there  is  danger  of  reducing  the  map  so  much  in  size  be- 
tween photograph  and  final  illustration  that  the  pin  heads  will  appear  as 
indistinct  dots  on  the  complex  surface  of  the  map.  In  Fig.  193  a  map 
was  used  in  which  there  was  more  detail  than  really  necessary  or  desir- 
able for  a  clear  illustration.  In  justice  to  the  General  Electric  Review  it 
must,  however,  be  said  that  the  map  shown  in  Fig.  193  has  been  reduced 
in  size  and  made  smaller  than  it  was  in  the  original  print.  This  map 
could  not  be  reduced  further  without  danger  of  completely  losing  the 
pin  heads  in  the  gray  background  resulting  from  so  many  lines  on  the 
map. 

In  producing  an  illustration  like  Fig.  193  considerable  ingenuity 
must  be  used  to  make  two  or  more  classes  of  pins  show  out  distinctly 
in  zinc  cuts  which  can  be  printed  in  only  one  color.     The  pins  on  the 


t  LOCATION  OP 
V     OF  1000  HP.  AND  OVER 

AND 

^  POWER 

SECTIONS  OF  STREAMS 

LNI  THE 

"        •    Commercial  Deifelopments 
f,        m    Manuhcturing  Developments 
heav^Line  .'•v)  far  Stream,  indicates 
Xj'oughly'Section  having  power. 


General  Electric  Review 


Fig.  193.    Location  of  Water-Power  Developments  of  1,000  Horse  Power,  and  Over, 
and  Power  Sections  of  Streams  in  the  United  States 

The  original  of  this  map  would  have  pins  in  two  different  colors.  The  photograph  taken  from  the  map 
would  be  retouched  by  the  use  of  a  pen  so  that  squares  would  replace  dots  for  one  of  the  two  colors 
of  pms.     The  illustration  shows  a  contrast  of  dots  of  two  shapes  rather  than  dots  of  two  colors 

239 


240 


GRAPHIC    METHODS 


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MAPS   AND    PINS  241 

original  map  can  be  in  different  colors.  After  a  photograph  has  been 
made  of  the  pin  map  it  is  best  to  compare  the  photograph  with  the 
original,  and  then  to  make  squares  out  of  those  circles  which  represent 
a  certain  color  of  pin  on  the  original  map.  Squares  are  easily  made  by 
using  a  fine  pen  on  a  photograph  considerably  larger  than  the  cut  itself 
will  be.  When  the  final  dots  are  not  too  small  in  size  it  is  possible  to 
make  shapes  with  the  pen  such  as  triangles,  outline  circles,  etc.,  which 
can  be  distinguished  from  one  another. 

If  a  great  reduction  in  size  is  necessary  between  the  original  material 
and  the  finished  illustration,  extreme  care  must  be  used  to  have  all 
the  lines  on  any  original  drawing  wide  enough  to  stand  the  reduction 
in  line  thickness  due  to  the  decrease  in  size.  If  a  drawing  one  foot 
wide  is  photographed  down  to  an  illustration  three  inches  wide  the 
lines  will  be  only  one-quarter  as  thick  as  in  the  original  drawing.  Lines 
on  the  original  drawing  must  therefore  be  made  very  wide — in  fact, 
much  wider  than  is  ordinarily  considered  desirable  until  experience  has 
been  gained  from  several  disappointments  in  the  appearance  of  finished 
illustrations.  It  is  not  easy  to  find  maps  with  lines  sufficiently  heavy 
to  permit  of  the  great  photographic  reduction  usually  necessary  in 
making  illustrations  from  pin  maps  or  other  map  representations. 
Quite  often  it  is  necessary  for  the  person  making  a  map  chart  to  go 
over  by  hand  all  outlines  such  as  borders  and  the  divisions  between 
States,  counties,  etc.,  to  make  those  particular  lines  very  much  heavier 
than  on  any  map  which  can  be  purchased. 

A  reducing  glass  which  makes  everything  seen  through  it  appear 
smaller  is  almost  essential  when  many  maps  or  charts  must  be  repro7 
duced.  A  convenient  size  of  reducing  glass  has  a  single  lens,  about 
1^^  inches  in  diameter,  and  causes  objects  to  appear  from  one-half  to 
one-quarter  the  size  of  the  original.  The  amount  of  reduction  can  be 
varied  by  holding  the  glass  at  different  distances  from  the  original 
drawing.  In  order  to  tell  how  much  reduction  in  size  is  made  by  the 
glass  at  any  given  distance,  it  is  possible  to  look  at  the  original  object 
with  one  eye  and  through  the  reducing  glass  with  the  other  eye  so  that 
by  superimposing  the  two  images  their  length  may  be  compared.  When 
a  chart  has  ruled  lines,  as  co-ordinate  lines,  it  is  a  simple  matter  to 
superimpose  the  images  from  the  two  eyes  so  that  one  square  of  the 
original  equals  two,  three,  or  four  squares  of  the  image  seen  through  the 
reducing  glass.  When  the  two  images  are  thus  superimposed,  study 
can  be  made  of  the  thickness  of  lines  or  other  details  in  the  reduced 


242  GRAPHIC    METHODS 

size  so  that  a  decision  may  be  had  as  to  whether  the  drawing  will  safely 
stand  the  proposed  reduction  without  having  the  lines  made  heavier. 

Fig.  194  shows  about  the  extreme  limit  of  what  can  be  done  in  the 
making  of  pin  maps.  The  original  map  here  was  40  inches  wide  and 
66  inches  long.  Nevertheless,  the  map  shows  up  satisfactorily  in  the 
greatly  reduced  size  of  the  half-tone  because  care  was  taken  to  have  i 
very  wide  lines  and  little  detail  on  the  original  map.  Each  of  the  19,500 
pins  of  five  different  colors  had  a  head  diameter  of  ^32  inch.  It  must  be 
remembered,  that  most  of  these  pins  were  in  the  characteristic  blue 
colors  commonly  associated  with  the  Bell  Telephone  System,  and, 
because  blue  is  almost  impossible  to  photograph,  the  pins  do  not  show 
out  as  strikingly  as  they  would  if  other  colors  were  used.  The  black 
splotches  on  the  map  were  caused  by  the  predominance  in  those  areas 
of  pins  with  dark  blue  heads.  When  this  pin  map  was  made  there  was 
no  intention  of  taking  a  photograph  of  it.  A  much  more  distinct 
photograph  would  have  been  secured  if  pins  in  the  contrasting  colors 
of  red,  orange,  black,  green,  purple,  etc.,  had  been  chosen.  All  of  these 
would  have  shown  dark  in  the  photograph,  instead  of  white  or  light 
gray  like  the  pale  blue  pins  which  in  Fig.  194  were  used  in  the  greatest 
number.  j 

Fig.  194  was  photographed  at  an  angle.  The  eastern  half  of  the  " 
United  States  appears  smaller  than  true  scale  because  of  the  perspective 
in  the  picture.  The  perspective  view  shows  that  the  glass-head  pins 
had  long  shanks.  This  map,  costing  several  hundred  dollars  to  pro- 
duce, could  be  injured  severely  by  a  few  strokes  of  a  janitor's  feather 
duster.  If  short  pins  were  used  wuth  spherical  heads  in  contact  with 
the  map  there  would  be  no  danger  of  the  pins  being  misplaced.  An- 
other disadvantage  of  the  long  steel  pins  is  that  the  steel  portion  exposed 
to  the  atmosphere  is  likely  to  rust,  especially  in  cities  near  salt  water. 
Pins  with  short  needle-points  pushed  entirely  into  cork  composition 
or  corrugated  straw-board  have  little  opportunity  to  rust. 

Fig.  195  shows  a  convenient  map  scheme  by  which  different  places 
on  the  map  are  numbered  so  that  detailed  information  regarding  each 
may  be  obtained  from  the  annexed  tabulation  numbered  to  correspond 
with  the  pin  numbers.  In  this  scheme  we  have  all  the  advantages  of 
a  pin  map  without  the  confusion  of  too  many  data  on  the  surface  of  the 
map  itself.  The  illustration  of  Fig.  195  was  evidently  prepared  by 
hand.  Such  an  illustration  can,  however,  be  made  by  using  pins  like 
those  shown  in  Fig.  196,  or  like  pin  No.  20  in  Fig.  199.     This  latter 


i 


MAPS    AND    PINS 


243 


an. 

Giffiis  Falls  Port  Car.  Co. Gfem F»Ih, N.  T D.  4  H.  R.  R.... 

HtLDMBERo  Cem.  Co HowoCav»,N.  Y D.4  H.R.  R  ... 

Alben's  Am.  Pobi.  Cim.  Woem Ataai,  N.  Y N.  Y.  0.  4  H.  R. 

HmaoN  PoiiT.  Cm.  Co Hudjon,  N.  Y, N.  Y.  C.  4  H.  R.. 

~  "        "       "  ~"  ,N.Y: N.Y.C.4H.R.. 


per  day 
1,800 
200O 
4^00 


5.  Ehpdie  Port.  Cem.  Co Waraen*.  ? 

&  Catooa  La«  CsM.  Co Poctlaad  Point,  N.  Y L  V.  R.  R 1,800 

7.  Watlano  Port.  Cem.  Co W»yIand.N.Y lErie^ifR'     }  500 

8.  Marenoo  Port.  Cem  Co Caledonia,  N.  Y N.  Y.C  ........ .  600 

9.  VlTOEX  Port  Cem.  Co MoUtorfn,  Pa Penn.  R.  R 750 

10.  ALLEtrrowN  Port.  Cem.  Co EvansviUe,  Pa P.  4  R 2500 

11.  New  Castle  Port.  Cem.  Co Newcastle,  Pa P.  4  L.  E  250O 

12.  Catseill  Cem.  Co Cementon,  N.  Y N.  Y.  C.  4  H.  R  .  1,200 

13-  Jamestown  Port.  Cem.  Co Yorktown,  Pa Penn.  R.  R 3500 

14.  Sanddskv  Port  Cem  Co York,  Pa Penn  R.  H 1500 

15.  Secchitt  Cement  4  LuECa Security,  Hd West  MdTR.  R  .  2300 

16.  DNrvERSAL  Port.  Cem.  Co Untveraal,  Pa Penn.  R.  R •27.000 

17.  Lehiob  Port.  Cwi.  Co ». New  Castle,  Pa P.  4  L.  E.-.^....  •36.600 

18.  Ceejcbnt  Port.  Cem.  Co Wampum,  Pa P.  4  L.  E 3,600 

IS  PuckhornPort.  Cem  Co -..ManlKim,  W.  V».  ..„ ^.B.tQ.BLtL 

20.  DuMOND  Port.  Cem  Co „ Middle  Branc'i.  Ohio Penn.  R.  R     ....  150O 

21  Sandusky  Port  Cem.  Co Bay  Ridie,  Onio .L.S.4M.S     ...  1500 

2^  .\LMA  Cement  Co WclUton,  Oliio C.  H.  V.  4  T  . . . .  2,000 

23  Lehioh  Port.  Cem.  Co WelUton,  Ohio C.  H.  V.  4  T 'SP.EOO 

24  York  Port  Cem.  Co , Portsmouth,  Ohio N    4  W 1,200 

25.  Wasasb  Port  Cem.  Co  Stroh,  Ind L.  6.  4  M.S...".  150O 

26  Sandusky  Port.  Cem.  Co. .  „ Syracuse,  Ind Penn.  R.  R 1,500 

27.  Universal  Port.  Cem.  Co BuBneton,  Ind C.  1.  *  L  •27,000 

28  Lehigh  Port  Cem.  Co Mitchell,  Ind B.  *  0.  R.  R  ...  •36,600 

29.  Louisville  Cement  Co Speeds,  Ind B.  4  0.  R.  R...  2.000 

30  KosMos  Port.  Cem.  Co Ko^mosdaie,  Ky L.  4  N 1500 

31.  Virginia  Port.  Cem.  Co Fordwick,  Va Soul' ern  R.  R. ..  3300 

32.  Norfolk  Port.  Cem.  Corp Norfolk.  Va Southern  U  R. . .  3,000 

33.  Dixie  Poet.  Cem.  Co Richard  City,  Tenn A.  G.  S  R.  R , . . .  4,000 

34.  Southern  States  Port.  Cem.  Co Roc'.cmart,  Ga Southern  R.  R...  1.200 

35  Standard  Port.  Cem.  Co Leeds.  Ala Southern  R.  R...  1,200 

X  Castalia  Port.  Cem.  Co Castalia.  Ohio L.  S.  4  M.  S 2,000 

il  Superior  Port.  Cem  Co Superior,  Ohio C.  4  0 2,000 

38.  Ironton  Port  Cem.  Co Ironton,  Ohio C.  40 1000 


•Includes  all  i 


wncd  by  company. 


Data,  Chicago 


Fig. 


195.  Location  of  the  Portland  Cement 
Plants  of  the  Eastern  Portion  of  the  United 
States  in  191 1.  Below  the  Map  Is  a  Tabula- 
tion Giving  the  Name,  Address,  Capacity  and 
Shipping  Railroad  for  Each  Plant 

A  pin  map  like  this  can  be  quickly  made  up  by  using  pins 
such  as  are  pictured  in  number  20  of  Fig.  199  or  pins  such 
as  are  used  in  Fig.  196.     An  outline  map  with  the  pins  can 
illustration  like  the  above 


pin  has  black  figures  on  a 
white  background,  and  does 
not  give  as  striking  an  effect 
as  white  figures  on  a  black 
ground. 

Fig.  196  gives  a  hint  of 
what  may  be  done  to  pre- 
pare advertising  copy  with 
almost  no  expense.  The 
illustration  was  made  direct 
from  a  map  on  which  pins 
were  used  having  black 
areas  lettered  in  white.  The 
only  hand  drawing  neces- 
sary for  this  illustration 
was  about  one  minute's 
work  in  darkening  the  high 
lights  where  there  were  re- 
flections from  the  surface 
of  the  black  pins.  An  illus- 
tration of  this  type  to  show 
the  location  of  agencies, 
branches,  etc.,  makes  effec- 
tive advertising  because  the 
black  spots  are  so  large  in 
comparison  with  the  size  of 
the  map  that  the  whole 
territory  of  the  United 
States  appears  to  be  well 
covered  by  agencies. 

Lettered  or  numbered 
pins  like  those  in  Fig.  196 
and  in  Fig.  199  are  fre- 
quently desirable  to  show 
the  daily  whereabouts  of 
salesmen,  repair  men,  etc., 
in  order  that  the  nearest  man 
may  be  telegraphed  to  in 

be  photographed  directly  to  produce  an 


244 


GRAPHIC    METHODS 


case  of  emergency.  One  prominent  manufacturer  of  locks  for  bank 
vaults  uses  a  map  which  shows  at  all  times  the  location  of  each  of  some 
fifty  bank-lock  experts  who  are  routed  from  city  to  city  each  day  by 
telegraph.  The  locations  of  the  pins,  and  the  railroad  lines  repre- 
sented on  the  map,  show  instantly  which  man  can  best  be  sent  to  any 
bank  which  reports  trouble  regarding  the  door  of  its  safe-deposit  vault. 
Letters  or  numbers  on  the  pins  indicate  the  name  of  each  man  so  that 
there  is  no  danger  of  an  error  such  as  might  occur  if  the  pins  were 
colored  uniformly  without  specific  letters  or  numbers. 


i\ 

_  J -'^^.>^_  ^ 

...5l^v  ,„-^""  / 

i                     .   "^      —■^  '" 

t£0i\ 

A 

"■7         —^ 

'■-■ir-        .^„        ■ — 

fc^jij 

1= — .  ":~' 

^—^ — '=T?--' 

Z^ 


(p^^-:p€4 


\ 


Fig.  196.     Map  to  Show  the  Location  of  the  Selling  Branches  of  a  Large  Manufacturing 

Company 

This  line  cut  was  made  directly  by  photographing  a  standard  map  in  which  standard  map  pins  had  been 
inserted.  Black  pins  with  white  letters  or  numbers  give  excellent  advertising  copy  with  absolutely 
no  drafting  work  required 

The  argument  of  Fig.  197  would  have  been  brought  out  better  if 
the  railroad  tracks  had  been  drawn  in  heavy  black  lines  across  the  city 
map.  Unless  one  is  familiar  with  the  city  of  Indianapolis,  there  would 
be  no  way  of  explaining  the  heavy  soot  deposits  in  that  section  shown 
on  the  lower  portion  of  the  map.  Even  the  mention  of  railroad  tracks 
in  the  title  does  not  make  up  for  not  showing  them  on  the  chart. 

In  preparing  Fig.  198  a  scale  was  very  carefully  selected  to  use  one 
dot  to  represent  a  definite  number  of  people  so  as  to  avoid  having  dots 
crowd  each  other  too  closely  on  the  map.  A  map  of  this  kind  could  be 
made  in  a  very  large  size,  and  then  be  reduced  photographically  to  a 


MAPS    AND    PINS 


ie4i 


size  which  could  be  used  in 
a  report  or  magazine  article. 
The  reduction  must  ordi- 
narily be  so  great  for  such  a 
map  that  considerable  fore- 
thought and  care  must  be 
used  or  the  dots  will  not 
show  up  distinctly  enough 
in  the  final  illustration. 
Anyone  w  ishing  to  see  many 
maps  of  this  type  shown  in 
very  excellent  manner 
should  consult  Volume  II  of 
the  Report  of  the  Transit 
Commissioner,  of  the  City  of 
Philadelphia,  published  in 
July,  1913. 

In  placing  dots  for  out- 
lying districts  on  maps  made 
by  the  method  of  Fig.  198, 
judgment  must  be  used  to 
have  each  dot  placed  at  ex- 


•  •  • 

•  •  • 

•  •  • 


•  •  • 

•  •  •  • 

•  •  • 


•  •  • 

•  •  •  I 

•  •  • 


•  •  • 

•  •  • 


•  •  •• 

•  •  •  • 

•  •  •• 


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0*0 


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«  • 


i'Ml 


•  •  •  • 

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^17 


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•  •••• 
•  •«• 

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:::»: 


William  D.  McAbte  in  the  Siirvej/ 

Fig.  197.    Relative  Soot  Deposits  in  Indianapolis, 
March,  1912 

The  greatest  soot  fall  is  in  the  vicinity  of  railroad  tracks 
Carefully  selected  samples  of  snow  were  melted  and  the  soot 
of  twenty-four  hours  weighed  after  the  water  was  evapora- 
rated.  Spot  maps  of  this  kind  can  be  quickly  made  by 
using  short  map  pins  pushed  in  till  the  pin  heads  touch 
the  map 


actly  the  right  point  to  locate  accurately  the  people  represented.  In  Fig. 
198  each  dot  represents  two  hundred  people.  A  dot  in  the  suburbs 
may  therefore  represent  all  the  people  in  one  square  mile  of  territory. 
If  a  map  were  first  made  with  two  hundred  dots  for  the  two  hundred 
people,  the  one  dot  actually  used  on  the  final  map  would  have  to  be 
placed  not  at  the  geographical  center  of  the  area  represented,  but  at 
the  center  of  gravity  of  the  two  hundred  dots  which  it  replaces. 

In  Fig.  199  various  combinations  are  shown  of  pins,  beads,  etc., 
of  use  in  map  work.  Data  for  map  presentation  are  frequently  so 
complex  that  ingenuity  is  taxed  to  show  the  facts  on  any  map  of  a 
size  commercially  available.  A  great  variety  of  effects  may  be  se- 
cured, however,  by  means  of  the  devices  shown  in  Fig.  199.  The 
exhibits  given  in  the  illustration  are  as  follows: 

1.  Long  pin  with  small  size  glass  head,  available  in  many  colors. 

2.  Long  pin  of  brass  wire  for  use  with  beads  as  shown  in  No.  9. 

3.  Long  pin  with  glass  head  used  in  conjunction  with  a  piece 
of  sheet  celluloid  cut  into  the  shape  of  a  flag. 


24G 


GRAPHIC   METHODS 


PROPOSED    ROUTES 
COMPREHENSIVE    SYSTEM 


PASSENGER      SUBWmTS 

rOftTME 

CITY  OF  CHICAGO 

OI.30 
POPULATO*  TAKEN  rSOM  uS  CENSUS  CF  00 

£*oi  ojTdPRtatNTs  aoo  people 


FTirTs  1  ?  i  i 


The  Engineering  Magazine 

Fig.  198.    Proposed  Routes  for  a  Comprehensive  System  of  Passenger  Subways  for 

the  City  of  Chicago 

On  this  map  each  dot  is  carefully  located  to  represent  200  of  the  population.  A  spot  map  of  this  kind,  made 
to  some  scale  whereby  one  dot  represents  several  people,  is  essential  to  any  reliable  study  of  transit 
facilities.  After  the  spot  map  is  made,  the  transit  routes  can  be  laid  out  to  give  the  best  service  possible. 
Short  map  pins  with  heads  touching  the  paper  can  be  used  for  dots  on  the  original  map 


MAPS   AND    PINS 


247 


irop 


I 


f 


m 


8     9     10     U 


t 


e 


#     m 


■m, 


12     15    14    15    16     n 


52 


V 


y 


18      19        20     21         22      23 


Fig.  199.    A  Full-size  Illustration  Showing  Some  of  the  Different  Arrangements  of 
Map  Pins  and  of  Beads  Which  Can  be  Used  for  Map  Work 

The  size  of  the  various  beads  and  pins  can  be  determined  by  measuring  on  the  above  picture  with  an  ordi- 
nary ruler,  as  the  articles  are  shown  in  their  exact  size 

4.  A  celluloid  flag,  with  beads  above  the  flag  to  represent  quan- 
tity, or  beads  in  different  colors  to  denote  various  characteristics 
for  the  data  portrayed.  The  grip  of  the  sheet  celluloid  on  the  pin 
is  sufficient  to  hold  both  the  beads  and  the  ffag  at  the  upper  part 
of  the  pin. 

5.  Long  pin  with  large  size  glass  head,  obtainable  in  different 
colors. 

6.  Pin  like  that  shown  in  No.  5  used  with  beads  strung  upon  it. 

7.  A  brass  tack  large  enough  to  receive  gummed  labels  which 
n  ry  be  written  upon  with  a  pen. 


248  GRAPHIC    METHODS 

8.  Map  pins  having  sharp  points  and  small  spherical  glass  heads 
in  contact  with  the  map.  These  pins  are  available  in  many  dif- 
ferent colors;  the  upper  one  in  No.  8  is  red  and  the  lower  one  blue. 

9.  Beads  in  various  colors  of  a  size  to  correspond  with  the  map 
pins  in  No.  8.  Here  the  beads  were  red.  White  beads,  used  for 
every  tenth  position,  show  at  a  glance  that  there  are  22  beads  on 
the  pin.     Note  that  the  color  red  photographs  as  black. 

10.  Map  pins  having  sharp  needle  points  and  spherical  glass 
heads  in  contact  with  the  map.  The  pin  is  of  the  same  general 
style  as  No.  8  but  it  has  a  head  of  larger  diameter.  This  pin  is  ob- 
tainable in  many  colors. 

11.  Cloth-covered  map  tacks  available  in  plain  colors  and  in 
plaids. 

12.  Single  bead  used  with  an  ordinary  pin  as  a  crude  substitute 
for  a  regular  map  pin. 

13.  Beads  in  different  colors  corresponding  in  size  with  the  map 
pin  of  No.  10. 

14.  Beads  of  two  different  sizes  representing  different  things 
but  at  the  same  location. 

15.  Beads  of  two  different  sizes  and  three  different  colors.  Since 
both  sizes  and  colors  may  be  varied,  and  almost  any  number  of 
beads  used  on  one  pin,  there  are  practically  unlimited  possibilities 
for  the  showing  of  complex  data. 

16.  Beads  on  a  pin  which  holds  down  on  the  map  a  sheet  of 
colored  celluloid  cut  to  the  exact  shape  of  a  small  land  area  to  which 
attention  is  directed. 

17.  A  sheet-celluloid  marker  held  by  a  map  pin  like  that  seen 
in  No.  8. 

18.  Celluloid-covered  tack,  available  in  different  colors. 

19.  Celluloid-covered  tack  with  stripes  of  different  colors. 

20.  Celluloid-covered  tack  with  printed  numbers  from  1  to  99 
inclusive. 

21.  Celluloid-covered  tack  having  a  rough  surface  so  made  that 
the  surface  may  be  written  upon  with  pencil  or  pen,  yet  erased 
afterwards  or  rubbed  off  with  a  moist  cloth.  Lettering  may  be 
made  permanent  by  means  of  a  coat  of  varnish. 

22.  Large  size  celluloid-covered  tack  available  in  different  colors. 

23.  Large  size  celluloid-covered  tack  with  stripes  of  different 
colors. 


MAPS    AND    PINS  249 

24.  Very  large  size  celluloid-covered  tack. 

It  will  be  seen  from  the  foregoing  list  that  the  possibilities  for 
ingenuity  in  map  and  pin  presentations  are  almost  unlimited.  The 
celluloid-covered  tacks  having  large  flat  heads,  shown  in  Nos.  18  to  24 
inclusive,  are  not  as  generally  used  as  they  might  be  for  map  work. 
Map  pins  and  tacks  of  this  sort  placed  upon  the  surface  of  a  map 
can  give  a  spot  map  with  any  desired  diameter  of  spots,  no  matter 
what  size  of  map  is  used  or  what  the  amount  of  photographic  reduc- 
tion may  be.  It  is  simply  a  question  of  selecting  from  the  spherical 
heads,  8  or  10,  and  the  flat  heads  18,  22,  and  24,  to  determine  which 
size  head  is  best  suited  to  the  size  of  the  original  map  and  to  the  size 
of  dot  desired  in  the  finished  illustration.  Large  celluloid-covered 
tacks  18,  22,  and  24  are  also  valuable  to  show  the  location  of  main 
offices  and  different  factories,  or  the  locations  of  particularly  im- 
portant distributing  points.  The  pins  numbered  8,  10,  18,  22,  or  24, 
are  five  different  sizes  of  pins  which  may  be  used  simultaneously  on 
the  same  map  to  show  different  degrees  of  importance  in  the  things 
represented. 

When  used  for  photographing  to  produce  an  illustration  such  as 
is  shown  in  Fig.  196,  lettered  or  numbered  pins  should  have  a  black 
background  so  that  the  black  circle  outlining  the  tack  head  will  show 
out  in  clear  contrast  against  the  map  itself.  This  requires  white 
figures  on  a  black  or  red  background.  Pins  having  red  letters  on  a 
black  background  cannot  be  used  for  photographing,  as  the  red  letters 
would  photograph  black  and  disappear  entirely,  leaving  a  solid  black 
circle  instead  of  a  circle  with  figures.  Since  pins  with  a  black  back- 
ground and  white  figures  are  not  commonly  obtainable,  it  may  occa- 
sionally be  necessary  to  use  pins  like  No.  20  in  Fig.  199  having  black 
figures  on  a  white  background.  Sometimes  it  may  be  feasible  to 
draw  an  ink-line  circle  around  each  number  which  appears  in  the  photo- 
graph so  that  the  circles  will  be  on  the  copy  sent  to  the  engraver  who 
makes  the  zinc  plate. 

When  pins  must  be  used  to  locate  agencies,  stores,  or  other  things 
which  are  usually  concentrated  in  cities,  the  limitations  are  rigid 
because  all  pins  should  be  located  on  the  map  immediately  above  the 
point  representing  the  city.  Crow^ded  pins  usually  have  to  be  spread 
horizontally  over  a  wide  area,  and  when  so  spread  out  it  is  impossible 
to  tell  which  of  several  adjacent  cities  the  various  pins  may  represent. 
Fig.  200  depicts  what  w^as  done  in  one  case  to  get  over  this  difficulty. 


250 


GRAPHIC    METHODS 


.>  ',  *,-^--v^f4 


"Modern  I'hilanthropy" ,  W.  H.  Allen,  Dodd,  Mead  tt  Cu. 


Fig.  200.     Sources  of  the  First  3,000  Letters  of  Appeal  Sent  to  Mrs.  E.  H.  Harriman. 
These  3,000  Letters  Asked  for  $70,000,000 

Eight  different  kinds  of  pins  were  used  on  this  map  to  represent  different  kinds  of  appeals.  Long  pins  like 
those  seen  here  are  apt  to  fall  out  of  the  map,  and  thus  destroy  the  accuracy  of  the  record.  Note  the 
area  around  New  York  shown  on  a  larger  scale  at  the  right 

as  far  as  possible,  by  showing  the  more  thickly  crowded  district  as  a 
separate  area  on  a  larger  scale  placed  at  one  side  of  the  map. 

The  use  of  beads  in  conjunction  with  pins  overcomes  the  main  diffi- 
culties encountered  when  pins  alone  are  used.  Beads  may  be  placed 
one  above  each  other  on  long  pins  or  wires  so  that  each  pin  will  be 
exactly  in  the  point  on  the  map  for  each  city,  and  thus  portray  nu- 
merical data  by  map  location  more  accurately  than  possible  with  other 
methods.  The  adjoining  cities  can  be  clearly  discerned  by  means  of 
separate  columns  of  beads,  whereas  if  pins  alone  are  used  the  dif- 
ferent groups  of  pins  frequently  blend  so  as  to  be  indistinguishable. 
If  there  is  only  one  item  to  be  represented  in  a  town,  single  glass-head 
pins  may,  of  course,  be  used  in  conjunction  with  the  beads. 

When  there  are  several  units  in  a  town,  the  beads  strung  on  a 
long  pin  or  wire  can  be  counted  quickly  if  a  bead  of  a  different  color 
is  used  for  every  tenth  bead,  so  the  whole  column  may  be  counted  by 
tens  as  possible  in  Fig.  201.  A  bead  map  like  Fig.  201  should  be 
mounted  on  several  layers  of  corrugated  straw-board  to  allow  the 
long  pins  sufficient  depth  in  the  mounting  to  hold  fast.     For  this 


MAPS    AND    PINS 


251 


particular  map  six  layers  of  straw-board  were  used,  giving  a  total 
thickness  of  about  1^^  inches.  Though  this  mounting  made  out  of 
corrugated  straw  board  was  thick,  it  was  extremely  light  and  very 
convenient  to  handle. 


Harvard    •  - 
(Jniversity 


Fig.  201.  Residence  of  the  Men  of  the  Class  of  1907,  Harvard  University,  Six  Years 
After  Graduation.  The  Bead  Wire  for  Boston  Includes  All  Men  Living  within 
Twenty-five  Miles  of  the  City  Hall 

Beads  on  long  pins  and  wires  were  used  here  when  there  was  more  than  one  man  in  a  town.  A  white  bead 
was  used  on  the  wire  for  every  tenth  man.  Counting  from  the  top  by  tens,  the  exact  number  in  any 
city  can  be  seen  from  the  illustration.  711  men  are  represented  in  this  illustration  less  than  5  inches 
wide,  yet  the  number  in  each  city  can  be  counted  accurately 

If  long  columns  of  beads  must  be  used  as  in  Fig.  201  for  New 
York  and  Boston,  the  beads  may  be  strung  on  piano  wire  such  as 
may  be  secured  in  any  good  hardware  store.  The  piano  wire  should 
be  heated  in  a  gas  flame  so  as  to  remove  some  of  the  spring  temper. 
After  the  Avire  has  been  heated  it  can  be  straightened  and  it  will  re- 
main  straight    without   continually    springing   back   into   coil   form. 


252  GRAPHIC    METHODS 

Brass  wire  should  be  used  if  the  holes  in  the  beads  are  large  enough 
to  take  wire  of  a  diameter  sufficient  to  give  the  required  amount 
of  stiffness.  Brass  wire  is  not  as  stiff  as  steel  wire.  When  small  beads 
must  be  used  having  small  holes,  the  combination  of  wire  and  beads 
may  be  given  several  coats  of  varnish,  if  necessary,  to  make  a  tall 
bead  column  stand  up  straight.  The  columns  for  Boston  and  New 
York  in  Fig.  201  had  to  be  varnished  as  the  wire  was  very  small  on 
account  of  the  fact  that  the  diameter  of  the  beads  was  only  about 
-A  inch. 

The  bead  map  in  Fig.  201  gives  a  great  quantity  of  information 
in  a  small  amount  of  space.  The  illustration  depicts  the  whole  United 
States  on  a  page  width  of  only  oj/g  inches,  yet  all  the  facts  represented 
by  the  beads  are  brought  out  clearly.  The  men  of  the  group  por- 
trayed who  reside  in  foreign  countries  are  indicated  by  pins  near 
the  seacoast  with  arrows  pointing  toward  the  country  of  residence. 
The  fact  that  there  were  large  numbers  of  the  men  in  Massachusetts 
made  necessary  an  extremely  long  wire  for  the  beads  of  the  Boston 
district.  Because  of  the  small  size  of  the  finished  illustration  and  the 
size  of  map  available,  large  diameter  beads  could  not  be  used,  and  the 
bead  wire  for  the  Boston  district  was  necessarily  very  tall  and  slender. 
The  Boston  bead  column  was  about  as  tall  as  could  be  used  without 
the  column  of  beads  bending  under  its  own  weight,  even  with  the 
bead  column  varnished. 

Another  difficulty  in  having  very  tall  columns  of  beads  is  due 
to  the  fact  that  the  bead  map  must  be  photographed  at  an  angle  of 
about  45  degrees  in  order  to  show  a  good  picture  of  the  map. 

If  the  bead  column  projects  more  than  a  reasonable  distance 
from  the  map  it  is  impossible  to  find  a  camera  lens  which  will  keep 
in  focus  the  whole  map  and  the  full  length  of  the  bead  columns.  Either 
the  map  or  the  top  of  the  bead  column  will  be  out  of  focus  and  there 
is  no  way  of  overcoming  the  difficulty.  When  Fig.  201  was  photo- 
graphed the  image  on  the  ground  glass  of  the  camera  showed  at  once 
that  the  tops  of  the  bead  columns  were  out  of  focus.  The  bead  wires 
for  New  York  and  for  Boston  were  accordingly  pulled  entirely  out  of 
the  map  and  the  map  was  photographed  Avithout  these  two  bead 
wires.  The  two  bead  columns  were  drawn  in  by  hand  on  the  surface 
of  a  photograph  measuring  8  inches  across  the  base  of  the  map.  With 
a  little  care,  using  a  fine-pointed  pen,  bead  columns  such  as  these  can 
be  drawn  in  so  that  the  ordinary  observer  would  jiever  notice  that 


1 


MAPS   AND    PINS  253 

they  were  put  on  after  the  photograph  itself  had  been  taken.  The 
angle  at  which  the  tall  bead  columns  should  slant  can  be  determined 
by  observing  other  bead  columns  in  the  same  vicinity.  In  the  case 
of  Fig.  201,  the  angle  was  obtained  by  observing  the  bead  column 
for  Philadelphia.  The  reduction  in  size  from  the  photograph  on  which 
the  hand  drawing  was  done,  to  the  half-tone  (in  this  case,  a  final  re- 
duction of  from  8  inches  to  4M  inches)  was  sufficient  to  eliminate 
most  of  the  imperfections  due  to  hand  work. 

The  use  of  beads  opens  up  a  whole  new  field  for  map  presentation 
of  statistical  data.  The  Board  of  Sanitary  Control  for  the  Cloak 
and  Suit  and  the  Dress  and  Waist  Industries  of  New  York  city  made 
up  two  bead  maps  showing  the  fire  risks  and  the  sanitary  condition 
in  all  the  twenty -five  hundred  factories  which  come  under  the  super- 
vision of  that  Board.  One  bead  on  the  map  represents  the  condition 
for  each  factory.  On  the  fire  map  the  height  of  the  multi-story  loft 
buildings  in  which  the  different  factories  may  be  found  is  indicated 
by  using  one  bead  for  each  floor.  Thus,  in  some  of  the  taller  build- 
ings, twenty  stories  are  indicated.  Different  colors  of  beads  according 
to  the  fire  risk  or  the  sanitary  defect  to  be  shown  mark  the  stories 
very  plainly,  and  the  heights  of  the  bead  columns  show  the  heights 
of  the  buildings  so  that  the  bead  map  itself  represents  in  miniature 
the  sky  line  so  typical  of  Manhattan  Island. 

Bead  maps  carefully  made  up  should  be  of  great  use  in  preparing 
illustrations  for  advertising  purposes.  The  accuracy  of  a  bead  map, 
when  data  for  difl^erent  cities  must  be  shown,  is  much  greater  than  that 
of  a  map  on  which  only  pins  are  used.  The  bead  map  makes  possible 
the  giving  of  information  in  condensed  form  with  that  great  clearness 
and  accuracy  necessary  to  good  advertising.  It  can  safely  be  pre- 
dicted that  pictures  of  bead  maps  will  in  the  future  be  a  common 
thing  in  the  advertising  pages  of  magazines. 


Chapter  XIII 
CURVES  FOR  THE  EXECUTIVE 

WITH  the  exception  of  the  railroads,  there  are  relatively  few 
businesses  which  make  a  practice  of  plotting  curves  to  show 
operating  records  in  convenient  form  for  the  use  of  executives. 
Railroad  accounting  is  more  highly  standardized  than  accounting  in 
industrial  corporation  work.  The  standardized  method  of  accounting 
has  made  it  rather  easy  to  compare  the  operating  records  of  different 
railroad  divisions  and  of  different  railroad  systems.  It  is  probably  for 
this  reason  that  railroads  have  adopted  the  use  of  curves  for  operating 
records  so  much  more  extensively  than  have  industrial  or  mercantile 
businesses. 

The  upper  curve  in  Fig.  202  is  plotted  according  to  the  method  used 
on  many  railroad  systems.  In  this  form  of  plotting  a  month  may  be 
said  to  be  represented  in  the  middle  of  a  space  between  the  vertical 
lines.  Horizontal  lines  are  drawn  in  the  space  for  each  month  to  a  scale 
representing  the  figures  which  it  is  desired  to  chart.  Lines  are  then 
drawn  vertically  to  coincide  with  the  vertical  lines  of  the  co-ordinate 
paper,  and  they  join  the  horizontal  lines  of  different  months  in  such  a 
way  as  to  give  an  effect  like  that  of  a  stairway. 

Curves  for  the  same  data  plotted  by  the  method  shown  at  the  bottom 
of  Fig.  202  are  much  easier  to  read  than  those  plotted  by  the  step  method 
shown  in  the  upper  portion  of  the  illustration.  By  the  method  in  the 
lower  part  of  the  illustration  the  plotted  line  more  closely  approaches  a 
true  curve,  there  is  much  less  variation  in  the  direction  of  the  lines  from 
month  to  month,  and  the  general  trend  of  the  curve  line  is  easier  for 
the  eye  to  grasp.  Compare  the  two  curves  for  the  summer  months  of 
the  year  1909-10.  In  the  upper  curve  a  series  of  steps,  and  in  the  lower 
curve  an  almost  straight  line  from  April  to  September  inclusive,  indi- 
cate an  increase  by  fairly  equal  increments  during  those  months. 
Certainly  equal  increments  are  more  easily  represented  by  the  straight 

254 


CURVES  FOR  THE  EXECUTIVE 


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Fig.  202..    Total  Sales  of  the  "Metropolis"  Branch  House  of  the  "R.S.T."  Automobile 

Company  for  Three  Years 

These  two  curves  are  plotted  from  exactly  the  same  figures.  The  upper  curve  is  drawn  by  the  method 
still  used  by  some  railroads,  but  generally  going  out  of  use.  The  lower  curve  is  plotted  by  a  simpler 
method  which  should  be  universally  used 

line  as  in  the  bottom  curve  than  by  the  ragged  series  of  steps  shown 
in  the  upper  curve. 

Another  disadvantage  of  the  method  of  steps  with  flat  tops  as 
compared  with  the  method  using  slanting  lines  and  peak  tops,  is  seen 
when  two  or  more  curves  are  so  drawn  that  they  intersect  on  the  same 
sheet  of  co-ordinate  paper.  Curves  plotted  with  peak  tops  can  be 
drawn  very  close  together  and  yet  be  fairly  distinct  from  each  other,  as 
will  be  noticed  in  many  of  the  illustrations  in  this  book.  If,  however, 
two  curves  with  flat  tops  like  those  shown  in  the  upper  portion  of  Fig. 
202  are  plotted  in  such  manner  that  they  intersect  each  other,  the  re- 


256 


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Fig.  203.    Lubrication  Cost  per  Ton  of  Product  for  a  Factory  in  the  Year  1908 

The  figures  at  the  top  of  the  co-ordinate  ruling  give  the  data  from  which  the  curve  was  plotted.  Though 
data  should  be  put  on  all  charts,  figures  arranged  in  the  direction  here  shown  are  not  in  convenient  form 
for  addition.  See  the  later  illustrations  in  this  chapter  for  methods  of  placing  figures  above  each  point 
on  a  curve 

suit  is  very  confusing  on  account  of  the  fact  that  the  vertical  lines  con- 
necting the  flat  tops  may  coincide.  When  one  line  falls  directly  on  top 
of  the  other,  there  is^  no  way  for  the  reader  to  judge  which  curve  is 
which  beyond  the  point  of  intersection.  Unless  the  curves  are  very 
carefully  colored  or  dotted  there  is  great  danger  that  the  reader  will 
jump  from  one  curve  to  the  other  in  his  interpretation  of  curves  which 
happen  to  meet.  This  weak  point  in  the  flat-top  method  is  particularly 
noticeable  if  blue  prints  must  be  made  from  original  charts  in  which  the 
flat-top  method  is  used.  On  the  original  chart  the  curves  can  be  fairly 
well  distinguished  by  using  different  colored  inks,  but  as  the  colors  are 
lost  in  blue-printing,  each  blue  print  must  be  colored  by  hand,  using 
the  original  chart  as  a  key  to  show  what  the  colors  should  be.  If  a  peak- 
top  method  of  plotting  is  used,  numerous  curves  may  be  run  across  the 
same  sheet  and  yet  be  distinct  enough  for  identification  even  when  all 
are  reduced  to  uniform  white  lines  on  the  blue  print.  It  would  be  easy 
to  name  fifteen  reasons  why  the  method  of  plotting  with  peak  tops  is 
superior  to  the  method  of  plotting  with  flat  tops.  The  advantages  of 
the  peak-top  method  seem  so  obvious  that  it  is  believed  the  reader 
will  agree  to  its  desirability,  without  further  argument  being  given  here. 
The  man  who  plots  a  curve  has  before  him  the  data  showing  the 
actual  value  for  each  point  plotted  on  the  curve.  If  any  questions 
arise  in  his  mind  regarding  the  comparative  figures  at  different  points 
on  the  curve,  he  can  refer  to  the  data  from  which  the  curve  was  plotted. 


CURVES    FOR    THE    EXECUTIVE 


257 


CALENDAR     YEAR 


1912  o 

1913  • 

Bureau  of  Railway  Economics,  Washington,  D.  C. 

Fig.  204.  Monthly  Revenue,  Expense, 
and  Net  Revenue  per  Mile  of  Line 
for  Railroads  in  the  United  States 
Having  a  Yearly  Revenue  of  One 


The  man  who  reads  the  curve,  how- 
ever, must  ordinarily  get  the  value 
of  any  point  on  the  curve  by  refer- 
ring to  the  scale  on  tlie  left-hand 
margin  of  the  chart.  As  most  points 
on  curves  do  not  fall  exactly  on  the 
horizontal  co-ordinate  lines,  the  only 
way  in  which  the  actual  value  at 
any  point  can  be  determined  is  by 
careful  estimate  of  the  fractional 
distance  between  horizontal  lines, 
according  to  the  scale  shown  on  the 
margin.  The  resulting  value  for 
the  point  is  ordinarily  more  or  less 
inaccurate,  depending  upon  the  scale 
to  which  the  curve  is  drawn.  Not 
only  is  the  reader's  time  taken  in 
estimating  the  value  for  any  point 
on  the  curve,  but  when  he  gets  his 
result  he  is  dissatisfied,  for  he  cannot 
feel  that  the  figure  obtained  is  really 
accurate.  There  is  a  great  advan- 
tage in  showing  on  a  chart  the  figures 
from  which  the  curve  was  plotted. 
When  only  one  curve  is  shown  on  a 
chart  it  is  very  easy  to  give  the 
figures  immediately  above  each  point. 
The  method  used  to  show  the  figures 
in  Fig.  203  is  not,  however,  satis- 
factory, as  the  figures  do  not  fall 
in  a  column.  The  method  of  indi- 
cating figures  shown  in  the  illus- 
trations later  in  this  chapter  is  much 
superior  to  the  method  of  Fig.  203,  and 
should  be  adopted  as  general  prac- 
tice by  anyone  preparing  curves  for 
record  purposes,  or  for  executive  use. 


MilUon  Dollars  or  More 

This  illustration  shows  one  of  the  difficulties  encountered  when  curves  for  successive  years  are  plotted  on 
the  same  co-ordinate  ruling.  Here  the  data  of  January,  1913,  are  indicated  by  a  dot  rather  than  by  a 
line.  The  change  occurring  from  December  to  January  is  not  easily  seen.  This  difficulty  can  be 
easily  overcome  by  allowing  an  extra  space  for  one  month  as  in  the  following  illustrations 


258  GRAPHIC    METHODS 

In  Fig.  205  a  curve  is  shown  drawn  upon  a  carefully  designed  four-by- 
six-inch  card  form.  This  card  is  designed  for  the  plotting  of  data  for 
one  year  by  months.  Thus,  the  fiscal  year  of  a  business  can  be  shown 
on  one  card.  Succeeding  years  are  entered  on  different  cards,  so  that 
by  arranging  the  cards  chronologically  variations  from  year  to  year 
may  easily  be  seen.  In  order  to  avoid  the  difficulties  pointed  out  for 
Fig.  204,  and  Fig.  104,  thirteen  vertical  lines  are  used  on  this  four-by- 
six-inch  card.  At  the  beginning  of  each  card  the  last  month  of  the 
previous  fiscal  year  is  repeated.  In  Fig.  205  the  fiscal  year  begins  in 
August.  At  the  beginning  of  the  card  we  repeat  the  line  for  July,  so 
that  instead  of  showing  a  dot  when  the  August  figures  are  plotted  we 
are  able  to  draw  a  line  showing  the  change  which  has  occurred  from 
July  to  August.  In  general,  it  is  good  practice  to  use  one  more  vertical 
line  than  there  are  points  to  be  plotted,  so  that  the  last  point  on  one 
curve,  sheet  or  card  may  be  repeated  on  the  next  curve  sheet  or  card. 

Figures  representing  the  value  for  each  point  on  the  curve  are  given 
immediately  above  each  point,  in  the  case  of  Fig.  205  to  the  nearest 
dollar.  Figures  for  cents  could,  of  course,  be  given  if  desired,  but  for 
executive  purposes  it  is  usually  better  to  neglect  the  cents  in  all  large 
numbers.  The  arrangement  of  the  figures  shown  in  Fig.  205  is  such 
that  at  the  end  of  the  year  the  figures  can  be  added  quickly  and  the 
total  given  on  the  card.  Cards  for  different  years  can  easily  be  looked 
over  and  the  yearly  total  figures  compared  instantly,  to  the  great  ad- 
vantage of  the  executive  who  has  these  additions  made  for  him  and 
recorded  where  they  are  always  in  plain  sight.  Curves  as  they  were 
used  in  the  past  gave  the  values  of  single  points  only,  without  any 
summation  for  a  series  of  points.  In  Fig.  205  we  have  not  only  the 
yearly  total,  but  also  totals  for  every  three  months,  so  that  the  total 
for  any  quarter  of  the  fiscal  year  can  be  compared  with  the  total  for 
any  other  quarter. 

Fig.  206  represents  a  four-by-twelve-inch  card  used  to  plot  data  for 
fifty -two  weeks  in  one  fiscal  year,  the  last  point  of  the  preceding  year 
being  repeated  at  the  left-hand  margin.  Figures  for  the  repeated  week 
are  not  given  above  the  co-ordinate  ruling,  as  the  repeated  figures  might 
then  be  included  in  the  additions  and  cause  serious  error.  By  repeating 
the  point,  however,  and  not  repeating  the  figures,  the  curve  is  made 
continuous  without  any  danger  of  adding  too  many  items  into  the  total. 

In  the  right-hand  margin  of  Fig.  206  a  short  vertical  line  may  be 
seen.     This  line  may  be  used  as  the  shank  of  an  arrow  to  indicate,  as 


CURVES    FOR    THE    EXECUTIVE 


269 


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CtJRVES    FOR    THE    EXECUTIVE  261 

in  Fig.  205,  in  which  direction  the  executive  desires  that  the  curve  should 
trend.  In  Fig.  205,  which  represents  total  sales,  the  head  of  the  arrow 
of  course  points  upward.  If  the  curve  is  to  show  expenses  per 
unit  of  output,  the  head  must  be  placed  on  the  vertical  line  so  that  the 
arrow  will  point  downward.  In  Fig.  206  no  head  is  placed  on  the  arrow, 
as  fluctuations  in  a  payroll  mean  nothing  unless  we  know  the  output  of 
work.  An  increasing  payroll  may  result  either  from  increasing  sales 
or  from  inefficient  production.  A  decrease  in  payroll  may  result 
from  increased  efficiency  of  production  or  because  sales  have  fallen 
off  undesirably.  Accordingly,  no  head  is  placed  on  the  arrow  and  the 
curve  must  be  interpreted  by  conditions  other  than  those  shown  on  the 
face  of  the  card  itself.  In  general,  all  curves  relating  to  total  money 
expenditures  may  trend  either  up  or  down,  without  meaning  anything 
unless  other  conditions  are  considered.  It  is  only  when  we  express 
expenditures  as  expenditure  per  unit  that  we  really  get  a  curve  for 
which  it  is  safe  to  say  that  we  should  always  desire  a  downward  trend 
as  long  as  quality  is  maintained. 

Forms  for  executive  records  such  as  are  shown  in  Fig.  205  and  Fig. 
206  should  be  printed  on  an  especially  high  grade  of  paper.  Most  paper 
in  use  to-day  contains  sulphite  pulp  and  chemicals  which  cause  more  or 
less  rapid  deterioration.  The  paper  commonly  used  turns  brown  and  gets 
brittle  within  five  or  ten  years,  so  that  records  on  this  paper  are  likely 
to  become  useless  in  a  comparatively  short  time.  High-grade  paper  to 
be  used  for  the  record  cards  shown  in  Fig.  205  and  Fig.  206  should  con- 
tain only  the  finest  selected  linen  stock  and  should  be  guaranteed  ab- 
solutely against  any  deterioration  for  twenty  years.  The  chief  advan- 
tage of  such  paper,  however,  is  that  it  can  be  used  in  card  form,  yet 
be  transparent  enough  to  allow  of  blue-printing. 

The  time  required  to  blue-print  cards  made  from  such  paper  may  best 
be  compared  with  the  time  necessary  when  ordinary  tracing  cloth  is  used. 
Blue  prints  are  also  frequently  made  from  bond  paper.  Bond  paper  re- 
quires an  exposure  of,  roughly,  three  times  as  long  as  tracing  cloth. 
A  special  card  made  of  heavy  paper  would  require  an  exposure  of  about 
six  times  as  long  as  tracing  cloth,  or  twice  as  long  as  bond  paper. 

When  sunlight  is  used  for  blue-printing,  there  is  no  diflSculty 
in  getting  a  sufficiently  long  exposure  to  make  good  blue  prints  from 
the  card  forms  shown  in  Fig.  205  and  Fig.  206,  if  the  forms  are  printed 
on  selected  paper.  Should  electric  blue-print  machines  be  used,  however, 
it  may  be  found  that  certain  of  the  older  types  of  continuous  printing 


262  GRAPHIC    METHODS 

machines  cannot  be  run  slowly  enough  to  give  the  required  length  of 
exposure.  Some  of  the  older  machines  can  be  changed  at  rather  slight 
expense  so  as  to  have  an  extra  belt-pullej^  reduction  between  the  motor 
and  the  blue-printing  machine  itself.  The  newer  types  of  machine 
can  usually  be  run  slowly  enough  to  give  the  exposure  necessary  for 
this  heavy  paper.  If  a  new  blue-printing  machine  is  to  be  ordered, 
however,  it  is  well  to  make  some  preliminary  tests  with  the  cards. 

The  cost  is  not  great  for  blue-printing  a  whole  set  of  record  cards 
once  each  month  after  the  last  data  have  been  plotted.  Blue-print 
paper  of  heavy  weight  should  be  carried  on  hand,  already  sensitized 
and  cut  to  size,  four  by  six  inches  and  four  by  twelve  inches.  The 
original  curve  cards,  each  backed  by  a  sensitized  card  of  the  same  size, 
are  simply  fed  into  the  blue-print  machine  as  rapidly  as  the  operator  can 
put  the  two  cards  together  in  pairs. 

There  is  a  tremendous  advantage  in  having  all  curve  records  made 
on  a  high-grade  transparciu  C-;rd  so  that  any  card  may  be  duplicated 
by  blue-printing  whenever  desired.  It  is  impossible  for  anyone  to 
predict  wdiat  conditions  will  come  up  in  the  future  of  a  business,  and 
the  only  safe  plan  is  to  install  from  the  start  such  a  curve-record  system 
that  any  card  may  be  duplicated  by  blue-printing  in  future  years  if 
desired.  It  frequently  happens  that  an  executive  wishes  to  have  a  blue 
print  made  of  a  recent  year's  curve  card  to  compare  with  the  curve 
card  of  an  earlier  year,  in  order  that  the  blue  prints  may  be  mailed  to 
some  higher  official  or  to  some  branch-house  manager  to  point  out  certain 
conditions  which  it  would  be  difficult  to  describe  fully  if  copies  of  the 
curve  cards  could  not  be  sent.  Unless,  however,  the  curves  for  the 
earlier  years  are  made  on  cardboard  from  which  blue  prints  can  be 
taken,  it  is  impossible  afterward  to  make  duplicates  of  these  cards 
except  by  hand  copying  or  photographing.  In  many  cases  it  will  be  found 
desirable  to  take  a  blue  print  of  every  record  card  once  each  month,  so 
that  blue  prints  may  be  sent  each  department  head  to  show  him  the 
exact  condition  of  his  department  as  a  guide  for  the  next  month. 

The  space  toward  the  left-hand  side  of  the  cards  shown  in  Fig.  205 
is  for  remarks  which  may  be  necessary  to  explain  different  fluctuations 
in  the  curves.  In  Fig.  206  full  circles  along  the  curve  show  those  w^eeks 
in  which  a  full  holiday  reduces  the  amount  of  the  payroll.  In  the  month 
of  April  there  was,  for  this  particular  plant,  a  half-holiday  on  the  nine- 
teenth. This  is  shown  by  a  half  circle.  At  the  end  of  the  fiscal  year  w^e 
see  in  Fig.  206  stars  to  explain  why  the  curve  showed  a  drop  to  less  than 


CURVES  FOR  THE  EXECUTIVE  263 

one-half  in  the  normal  size  of  the  payroll.  The  plant  was  shut  down  at 
the  end  of  the  fiscal  year  in  order  that  an  inventory  might  be  taken. 

The  notes  at  the  left-hand  side  of  the  card  are  absolutely  essential  to 
explain  unusual  conditions  affecting  the  curves.  In  two  years  after  an 
event,  most  managers  are  entirely  unable  to  explain  certain  peaks  or 
valleys  in  a  curve,  though  these  extreme  fluctuations  may  be  due  to 
such  events  as  fires,  floods,  or  strikes.  Unless  the  causes  of  unusual 
fluctuations  are  recorded,  the  curves  would  have  far  less  than  their 
possible  utility  to  any  new  man  who  must  take  up  the  manager's  task 
as  his  assistant  or  as  his  successor.  An  example  of  the  kind  of  informa- 
tion which  should  be  noted  on  the  curve-card  margin  came  up  in  a  large 
public-service  company,  where  the  manager  was  for  several  minutes 
unable  to  explain  a  very  great  fluctuation  which  had  affected  the  earn- 
ings of  a  trolley  company  some  two  years  before.  After  careful  study 
to  explain  the  drop  in  the  curve,  he  finally  recalled  that  this  trolley 
line  was  in  a  city  where  all  cars  must  pass  over  a  drawbridge  between 
two  sections  of  the  town.  At  the  time  in  question  a  steamer  had  col- 
lided with  the  drawbridge,  making  it  impossible  for  about  two  weeks 
for  any  street  car  to  cross.  This  accident  caused  the  earnings  of  the 
trolley  line  to  drop  greatly  during  the  whole  of  the  two- weeks  period. 
The  cause  of  the  unusual  condition  for  the  curve  should  have  been 
recorded  for  future  reference. 

In  Fig.  207  we  have  the  curves  for  three  succeeding  years  placed  one 
above  the  other,  so  the  eye  can  glance  up  and  down  the  vertical  lines 
for  months  and  see  instantly  the  changes  which  have  occurred  during 
the  entire  period.  As  automobile  sales  are  very  greatly  affected  by 
the  weather  conditions  of  different  seasons  of  the  year,  these  curves  are 
important.  Though  weather  conditions  have  affected  the  curves  quite 
largely,  we  can  see,  by  comparing  the  curves  for  1910  and  1911,  that 
probably  conditions  of  management  as  well  as  weather  conditions 
caused  smaller  shipments  in  November  and  December,  1911,  than  in 
those  same  months  of  1910,  when  shipments  were  quite  good.  The  card 
for  1912  is  shown  with  the  curve  incomplete,  just  as  the  manager  might 
have  seen  it  early  in  the  month  of  February,  1912,  after  the  January 
reports  had  been  received,  tabulated  and  plotted.  As  Fig.  207  shows 
curves  which  are  true  records  of  the  real  happenings  in  an  automobile 
plant,  they  are  worthy  of  study  for  practice  in  curve  interpretation. 
Notice  that  the  changes  from  July  to  August,  in  1911  and  1912,  are 
readily  seen  because  each  curve  card  begins  by  repeating  the  record 


264 


GRAPHIC    METHODS 


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Fig.  207.    Sales  of  the  "X.Y.Z."  Automobile  Plant  for  Three  Consecutive  Years 

The  three  4-by-6-inch  cards  are  arranged  one  above  the  other  so  that  the  curves  for  different  years  may  be 
easily  compared.  Note  that  November  and  December  were  good  months  in  1910,  but  poor  months  in 
1911  and  1912.  The  1911  card  above  is  the  same  as  in  Fig.  205,  but  here  it  is  printed  in  one  color 
only.  Observe  at  the  right  the  arrows  showing  that  it  is  desired  that  the  trend  of  the  curve  should  be 
upward.  Arrows  like  this  save  about  two-thirds  of  the  executive's  time  in  looking  over  a  large  numbe 
of  curves 


CURVES    FOR    THE    EXECUTIVE 


<^Q5 


for  the  last  month  of  the 
preceding  fiscal  year  in- 
stead of  using  a  dot  as 
shown  in  Fig.  204. 

The  separate  cards  for 
different  years,  which  in 
Fig.  207  are  arranged  ver- 
tically one  above  the  other, 
may  be  laid  horizontally  as 
in  Fig.  208.  Here  the  cards 
are  superposed  on  a  black 
background,  the  left-hand 
and  middle  cards  each  over- 
lying the  card  to  the  right, 
so  that  the  curve  appears 
continuous.  The  vertical 
arrangement  allows  of  a 
very  accurate  analysis  of 
changes  which  have  oc- 
curred from  month  to 
month  of  each  year.  With 
the  horizontal  arrangement 
it  is  not  so  easy  to  compare 
any  month  of  one  year  with 
the  corresponding  month  of 
another  year,  but  it  is  easier 
to  see  the  changes  which 
have  occurred  in  a  curve  as 
a  whole  throughout  a  period 
of  years.  Thus  in  Fig.  208 
it  is  much  easier  than  in 
Fig.  207  to  see  that  sales 
dropped  seriously  in  the 
first  half  of  1911,  and  that 
they  increased  far  beyond 
any  previous  record  during 
the  last  half  of  1911.  The 
vertical  arrangement  is  use- 
ful for  one  purpose :  the  hori- 


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^66  GRAPHIC    METHODS 

zontal  arrangement  is  useful  for  another  purpose.  By  having  loose 
cards,  we  can  arrange  the  cards  either  horizontally  or  vertically  and 
get  all  the  advantages  of  either  position.  Curves  plotted  in  loose-leaf 
books,  or  on  large  sheets  of  paper,  cannot  have  this  flexibility  of  arrange- 
ment, and  they  accordingly  handicap  the  executive  in  the  analysis 
of  data  which  may  be  vital  to  the  success  of  his  business. 

When  the  cards  are  arranged  horizontally  the  figures  for  the  curve 
over  a  series  of  years  are  in  plain  sight,  while  in  the  vertical  arrange- 
ment one  card  hides  the  figures  on  another  card.  Figures  are  essen- 
tial to  the  true  interpretation  of  curves  like  those  seen  in  Fig.  208. 
In  looking  at  Fig.  208  most  readers  are  hkely  to  feel  that  the  business 
of  the  year  1911  was  much  better  than  the  business  of  the  year  1910. 
When  we  look  at  the  total  figures,  however,  we  see  that  the  sales 
for  the  year  1911  were  only  $1,435,041,  while  the  sales  for  1910  were 
Jf>l  ,575,298.  Not  only  were  the  total  sales  for  1911  much  less  than  the 
sales  for  1910,  but  there  was  a  very  great  fluctuation  in  sales  from 
month  to  month  which  created  a  very  difficult  problem  in  the  opera- 
tion of  the  manufacturing  plant.  In  the  early  half  of  the  fiscal  year 
ending  in  1911,  men  were  not  needed  because  of  the  small  volume 
of  sales,  and  a  large  portion  of  the  working  force  had  to  be  discharged. 
In  the  latter  half  of  the  fiscal  year,  sales  increased  so  rapidly  that  men 
had  to  be  hired  in  large  numbers.  Inevitably,  therefore,  many  un- 
skilled men  were  obtained  who  were  sure  to  spoil  a  large  volume  of 
any  output  requiring  the  great  accuracy  needed  by  automobile  parts. 
The  record  for  the  fiscal  year  ending  1911  was  in  every  way  bad,  as 
compared  with  that  for  the  fiscal  year  1910.  The  company  eventually 
ended  in  a  receivership. 

Cards  only  four  inches  by  six  are  of  sufficient  height  to  hold  the 
co-ordinate  ruling  needed  for  curve  plotting,  and  yet  have  room  above 
the  ruled  field  for  two  separate  columns  of  figures  of  seven  digits 
each,  as  well  as  space  across  the  top  for  a  title  which  may  run  the  whole 
length  of  the  card.  In  Fig.  208  we  have  two  sets  of  figures,  one  set 
for  months  and  the  other  set  for  quarters.  Each  set  of  figures  con- 
tains six  numerals.  Although  the  illustration  in  Fig.  208  is  only 
about  one  half  the  natural  size  of  the  card,  the  figures  themselves  are 
clearly  legible  and  the  title  at  the  top  of  the  card  is  easily  read. 

One  of  the  chief  advantages  in  the  use  of  loose  cards  lies  in  the 
fact  that  any  set  of  cards  may  be  laid  out  on  a  table  and  compared 
with  any  other  set  of  cards  in  the  manner  shown  in  Fig.  209.     It  is 


CURVES  FOR  THE  EXECUTIVE  267 

difficult  with  a  loose-leaf  book  to  arrange  a  system  for  keeping  hun- 
dreds of  curves  in  such  a  way  that  quick  comparisons  between  any 
of  them  can  be  made.  When  loose  cards  are  used  any  card  can  be 
compared  with  any  other  card  instantly,  and,  if  desired,  cards  for  any 
curve  for  a  series  of  years  may  be  laid  out  for  comparison  with  cards 
for  any  other  curve  for  any  series  of  years.  Anyone  without  experi- 
ence in  the  analysis  of  curve  records  for  large  corporations  may  take 
it  as  a  fact  that  no  system  of  curve  records  should  be  installed  which 
does  not  permit  the  instantaneous  comparison  of  any  curve  with  any 
other  curve  in  the  whole  system. 

Fig.  207  and  Fig.  208  show  the  shipments  from  an  automobile 
manufacturing  plant  as  sales.  Many  of  the  automobiles  recorded 
as  sold  were  shipped  to  branch  houses  owned  by  the  same  company, 
to  be  stored  there  during  the  winter  months  when  the  branch-house 
sales  are  very  small,  for  the  reason  that  people  do  not  wish  to  buy 
touring  cars  in  winter.  In  Fig.  209  and  210  more  curve  records  from 
an  automobile  business  are  given.  In  these  cuts  also,  as  in  Fig.  207  and 
208,  cards  are  shown  in  groups  of  three,  photographed  against  a  black 
background.  In  Fig.  209  we  have  in  the  upper  curve  the  actual 
sales  of  an  automobile  branch  house  selling  direct  to  the  auto- 
mobile user.  Notice  that  the  sales  in  the  spring  months  greatly  ex- 
ceed the  sales  at  any  other  time  of  the  year.  In  the  first  two  fiscal 
years  sales  were  at  a  maximum  in  May,  while  in  the  third  fiscal  year 
sales  reached  the  maximum  in  April  ^nd  were  fairly  large  in  both 
March  and  May. 

In  the  lower  curve  we  have  the  expenses  of  this  same  branch 
house.  A  very  noticeable  increase  in  the  expenses  occurred  in  the 
fall  months  at  the  beginning  of  the  fiscal  year,  once  in  October  and 
twice  in  September.  This  increase  was  due  to  local  advertising  an- 
nouncing the  new-model  automobile  for  the  next  season.  It  was 
customary  for  all  manufacturers  of  automobiles  to  announce  their 
next  season's  models  in  the  fall  months,  and  the  peaks  in  the  expense 
curve  shown  here  came  as  they  did  simply  because  of  this  custom 
of  the  trade. 

It  is  quite  easily  seen  from  the  upper  curves  that  the  sales  for  the 
second  fiscal  year  were  much  greater  than  those  for  the  first  fiscal 
year.  The  total  figures,  however,  show  much  more  clearly  the  extent 
of  the  increase.  Because  of  the  excellent  sales  during  the  spring  months, 
the  curve  for  the  third  fiscal  year  at   the  right  gives  the  impres- 


268 


GRAPHIC    METHODS 


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sion  of  a  prosperous  year. 
Reference  to  the  figures  for 
the  total  yearly  sales,  how- 
ever, shows  that  the  sales 
for  the  third  year  increased 
only  very  slightly  over  the 
preceding  year.  When  we 
compare  the  sales  of  this 
branch  house  with  the  ex- 
penses, we  get  quite  a  dif- 
ferent story  from  that  read 
from  sales  curves  alone. 
The  increase  in  sales  from 
the  first  year  to  the  second 
year  was  very  great  and 
without  a  correspondingly 
great  increase  of  expenses. 
Putting  the  figures  for  the 
first  and  second  years  into  a 
ratio,  sales  increased  64  per 
cent,  while  expenses  in- 
creased only  10  per  cent. 
In  the  third  year,  however, 
the  sales  hardly  increased 
at  all,  while  the  shape  of 
the  curve  for  expenses 
shows  an  almost  constant 
increase.  A  little  mental 
arithmetic  will  show  further 
that  with  almost  stationary 
sales  the  expenses  were  per- 
mitted to  increase  about 
one-seventh  or,  roughly,  14 
per  cent. 

Notice  that  in  Fig.  209 
arrow-heads  mark  a  desire 
that  sales  should  go  up.  No 
arrow  was  used  in  connection 
with  the  curve  for  expenses. 


270  GRAPHIC    METHODS 

It  was  permissible  that  expenses  should  go  up  in  the  second  fiscal 
year,  for  the  volume  of  sales  increased  very  rapidly.  The  cost  per 
unit  of  sales  or  the  ratio  of  expenses  to  total  sales  had  decreased  greatly. 
An  arrow  pointing  downward  would  have  given  a  wrong  impression 
as  the  total  expenses  had  increased  justifiably.  It  is  better,  therefore, 
to  avoid  using  arrows  than  to  use  arrows  which  would  mean  nothing. 

The  real  story  of  this  automobile  branch  house  is  seen  in  Fig.  210 
which  gives  the  profit-and-loss  curve  corresponding  to  the  sales  and 
expense  curves  of  Fig.  209.  Expenses  of  the  branch  house  were  fairly 
large  throughout  the  whole  year,  because  of  fixed  charges,  while  the 
great  fluctuation  in  sales  caused  a  loss  during  the  many  months  in 
which  the  volume  of  sales  was  small.  Note  how  much  better  the 
profits  were  in  the  second  year  than  in  the  first  year,  because  the 
business  had  been  established  long  enough  to- have  a  fairly  good  vol- 
ume of  sales  during  the  fall  months.  There  was  a  profit  in  all  the 
months  of  the  second  year  except  two,  with  a  total  profit  of  very 
considerable  size,  though  not  a  tremendous  one  compared  with  the 
volume  of  sales,  since  the  profit  was  only  5.9  per  cent  of  the  sales. 
In  the  third  year  the  profits  were  on  the  ragged  edge  throughout 
the  whole  year  except  in  the  three  spring  months  of  March,  April, 
and  May  when  sales  were  exceptionally  large.  The  total  profits  for 
the  year,  even  with  a  slightly  increased  volume  of  sales,  were  less  than 
one-third  of  what  they  had  been  for  the  preceding  year. 

Just  to  show  what  complex  conditions  enter  into  the  comparison 
of  business  curves  of  this  sort,  it  is  mentioned  here  that  the  small 
volume  of  sales,  the  large  expenses,  and  the  negligible  profits  in  the 
first  half  of  the  third  fiscal  year  were  not  the  fault  of  the  manager  of 
this  branch  house.  The  trouble  went  back  to  the  factory  engineering 
department  which  failed  to  get  its  next  season's  models  designed  early 
enough.  Consequently  the  car  could  not  be  manufactured  in  suf- 
ficient quantities  to  give  the  branch  manager  enough  cars  to  make 
a  satisfactory  volume  of  sales.  The  branch  manager  blamed  the  factory 
because  the  factory  could  not  deliver  a  sufficient  quantity  of  cars.  The 
factory  manager  was  not  to  blame,  however,  as  the  engineering  depart- 
ment (reporting  direct  to  the  president  instead  of  to  the  factory  man- 
ager) had  delayed  the  design  for  the  new  car,  and  the  factory  manager 
was,  of  course,  unable  to  build  a  car  until  he  had  the  drawings.  This 
example  will  perhaps  give  a  fair  idea  of  the  uses  which  can  be  made  of 
curves  plotted  from  the  operating  figures  of  a  complex  business. 


CURVES    FOR    THE    EXECUTIVE  271 

A  person  who  has  not  tried  plotting  curves  on  cards  only  four  inches 
high  is  likel}^  to  saj^  that  the  card  is  not  of  sufficient  height  to  permit 
satisfactory  curve  plotting  when  there  is  a  great  fluctuation  in  the  curve. 
Such  a  person  would  argue  that  the  card  is  not  high  enough  to  allow 
the  plotting  of  curves  on  a  scale  sufficiently  large  for  easy  reading,  and 
that  any  curve  for  a  constantly  increasing  business  is  likely  to  run  off 
the  top  of  the  co-ordinate  ruling  within  a  few  years.  The  curves  as 
shown  in  this  chapter  certainly  vary  enough  to  allow  the  eye  to  see  all 
the  changes  clearly.  As  the  curves  are  in  each  case  accompanied  by 
the  actual  figures  for  the  value  of  each  point  on  the  curves,  it  is  not 
necessary  that  one  should  be  able  to  measure  accurately  for  points 
falling  between  horizontal  co-ordinate  lines.  Instead  of  consulting  the 
vertical  scale  to  get  the  value  at  any  point,  reference  is  made  to  the 
actual  figures  above  the  various  points.  These  figures  indicate  a  finer 
fluctuation  in  the  curve  than  it  is  possible  for  the  eye  to  appreciate 
even  in  curves  plotted  on  very  large  sheets  of  paper.  Figures,  then,  in 
conjunction  with  curves  like  those  shown  here,  make  it  unnecessary  to 
plot  lines  of  such  fine  width  or  great  accuracy  as  would  be  necessary 
if  the  figures  were  not  shown  above  the  curve. 

In  Fig.  207  the  bottom  card  shows  the  zero  line  extended  to  the  left 
over  the  figure  seven  at  the  lower  left-hand  corner  of  the  ruled  field. 
On  the  middle  card  the  zero  line  has  been  extended  to  the  right.  This 
right-and-left  extension  of  the  zero  line  is  not  made  until  a  card  has 
been  completely  filled  out.  The  extension  of  the  zero  line  indicates 
the  point  at  which  cards  are  to  be  joined  when  laid  in  the  horizontal 
position  shown  in  Fig.  208.  It  will  be  noticed,  in  Fig.  208,  that  the 
cards  are  overlapped  in  such  a  way  that  the  right-hand  edge  of  the 
uppermost  card  coincides  with  the  left-hand  edge  of  the  ruled  field 
of  the  lower  card,  and  that  the  zero  line  is  continuous.  The  extension 
line  drawn  at  the  left  of  any  lower  card  shows  where  the  extension 
drawn  across  the  right  margin  of  the  upper  card  is  to  be  joined.  Cards 
may  be  laid  together  in  a  horizontal  position  almost  instantly,  and  cor- 
rectly, when  these  joint  lines  are  present  as  a  guide. 

If,  as  in  Fig.  211,  a  curve  should  rise  with  such  rapidity  as  to  be 
dangerously  near  the  upper  limit  of  the  ruled  portion  of  the  card,  the 
joint  lines  may  be  so  drawn  as  to  allow  more  vertical  space  on  the  suc- 
ceeding cards.  In  Fig.  211  the  curve  for  1910  indicated  that  the  curve 
for  1911  might  go  higher  than  the  1,400  line.  Consequently,  when 
the  new  card  was  made  out  for  the  year  1911,  the  joint  lines  were  so 


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drawn  that  the  line 
at  the  right  of  the 

1910  card  was  above 
zero,  and  the  joint 
Hne  at  the  left  of  the 

1911  card  at  the  bot- 
tom   of    the    ruled 
field.      Thus,    when 
the    two    cards    are 
overlapped    so    that 
the  joint  lines  match, 
it  is  seen  that  there 
is   enough    space   in 
the  ruled  field  at  the 
right  for  the  curve  to 
rise  to  the  scale  line 
for  1,600.  Two  more 
spaces     were     again 
allowed   in    1912   in 
anticipation  of  even 
further  upward  pro- 
gress  in   the   curve. 
As  joint  lines  may  be 
drawn    in   continua- 
tion of  any  horizontal 
line    on    either    the 
upper  or   the   lower 
card,  any  amount  of 
expansion  in  future 
years    may   be   pro- 
vided for.  The  curve 
cards   are   small 
enough   to    be    very 
convenient  to  handle 
and    yet   they    may 
be  joined  together  in 
such    a    way    as    to 
provide  for  unlimited 
future  growth. 


CURVES  FOR  THE  EXECUTIVE  273 

The  card  for  1910  in  Fig.  211  has  a  broad  hne  drawn  by  hand  to 
show  the  zero  hne.  On  the  card  for  1911  the  scale  begins  at  400,  and, 
because  the  scale  does  not  begin  at  zero,  the  bottom  of  the  co-ordinate 
field  is  marked  with  a  wavy  line.  This  wavy  line  is  made  very  rapidly 
with  a  pen  and  serves  the  very  useful  purpose  of  safeguarding  the 
reader  from  interpreting  the  curve  as  if  the  lower  line  on  the  field  were 
zero.  Whenever  zero  is  not  shown  at  the  bottom  of  the  ruled  field, 
this  wavy  line  should  be  used.  Any  card  can  thus  be  read  independent- 
ly, with  safety  so  far  as  its  interpretation  from  the  zero  point  is  con- 
cerned. When  several  cards  are  laid  out  together,  and  the  zero  line  is 
shown  on  the  left-hand  card,  as  in  Fig.  211,  it  is  a  simple  matter  for 
the  eye  to  imagine  the  zero  line  extended  to  the  right  below  the  other 
cards,  thus  permitting  easy  interpretation  of  all  cards. 

It  sometimes  happens,  especially  in  plotting  costs,  that  the  desired 
direction  of  the  curve  will  be  downward  instead  of  upward.  In  such  a 
case,  and  to  show  small  fluctuations  from  month  to  month,  the  scale  on 
the  curve  cards  may  be  so  selected  that  the  zero  line  does  not  appear 
even  on  the  first  card  plotted.  Should  the  costs  be  reduced  so  rapidly 
that  the  curve  tends  to  run  off  the  bottom  of  any  card,  the  card  for  the 
succeeding  year  may  have  the  joint  line  drawn  in  such  a  way  as  to 
allow  an  extension  of  the  scale  downward,  exactly  as  Fig.  211  shows  an 
extension  of  the  scale  upward.  By  drawing  the  left-hand  joint  line 
on  the  later  cards  above  the  bottom  of  the  ruled  space,  and  by  putting 
the  right -hand  joint  lines  for  the  first  cards  at  the  bottom  of  the  ruled 
curve  field,  the  series  of  curves  can  be  made  to  progress  downward  to 
any  desired  extent  in  exactly  the  same  manner  as  the  curves  in  Fig.  211 
progress  upward  year  by  year.  By  the  use  of  these  joint  lines  a 
thoroughly  universal  arrangement  of  cards  may  be  secured,  allowing 
extra  space  for  movement  either  up  or  down. 

Joint  lines  were  devised  chiefly  to  permit  of  showing  a  large  up- 
ward or  downward  progress  in  the  curves  for  succeeding  years  with- 
out the  necessity  of  laboriously  replotting  the  curves  for  the  earlier 
years.  The  desired  result  has  been  very  satisfactorily  attained.  Should 
anyone,  however,  object  to  the  presenting  of  a  series  of  cards  in  steps 
as  in  Fig.  211,  he  need  only  replot  the  curve  for  the  earlier  years  to 
some  smaller  scale.  In  general,  however,  it  will  be  found  that  prac- 
tically no  replotting  is  necessary  or  desirable.  By  connecting  the  cards 
with  joint  lines  and  by  using  a  wavy  base  line  when  the  scale  does  not 
extend  to  zero,  all  necessary  convenience  and  accuracy  may  be  secured. 


274  GRAPHIC    METHODS 

When  plotting  curves  on  large  sheets  of  co-ordinate  paper  it  fre- 
quently happens  that  the  scale  desired  cannot  be  placed  upon  the 
kind  of  ruled  paper  available.  Scales  must  usually  be  made  in  full 
size,  one-half  size,  one-quarter  size,  etc.,  and  it  is  usually  too  big  a 
jump  to  change  from  one  of  these  sizes  to  another.  The  ideal  arrange- 
ment is  to  have  a  supply  of  co-ordinate  paper  with  different  rulings 
so  that  when  one  ruling  does  not  suit,  some  other  ruling  may  be  used. 
On  the  curve  cards  shown  in  this  chapter  the  horizontal  scale  is  fixed, 
as  the  cards  are  designed  for  use  with  definite  units  of  time,  such  as 
one  year  by  months,  one  year  by  weeks,  five  years  by  months,  etc. 
For  the  vertical  scale,  however,  two  different  rulings  are  provided. 
One  of  these  rulings  has  seven  i-inch  spaces  as  may  be  seen  in  Fig. 
211.  The  other  ruling  has  ten  vertical  spaces  of  i  inch  each  as  seen 
in  Fig.  209.  The  ratio  of  the  two  scales  is  seven  to  ten  or,  roughly, 
one  scale  may  be  said  to  be  two-thirds  of  the  other.  This  is  the  most 
desirable  arrangement  that  it  is  possible  to  get,  as  these  two  rulings 
afford  a  great  range  of  scales  to  choose  from.  If  by  using  one  ruling 
the  curve  comes  too  high  on  the  card,  simply  change  over  to  the  other 
ruling  and  the  peak  will  come  lower  down  on  the  card.  The  two 
rulings,  either  in  full  size  or  in  some  fractional  size,  give  every  pos- 
sible combination  of  scale  that  need  be  desired. 

The  ruling  having  vertical  spaces  of  one-sixth  of  an  inch  is  ten 
spaces  high.  This  rulin'g  is  very  convenient  for  curve  plotting  on  a 
percentage  basis  when  100  per  cent  is  shown  at  the  top  of  the  chart 
as  in  Fig.  126,  Fig.  128  and  Fig.  129  in  Chapter  IX.  If,  on  the  ten- 
space  card,  each  space  is  used  to  represent  10  per  cent  with  zero  for 
the  bottom  line  and  100  per  cent  for  the  top  line  of  the  chart,  the 
neatest  possible  arrangement  is  secured. 

In  starting  to  plot  a  curve  which  is  to  be  continued  year  after 
year,  it  is  ordinarily  best  to  allow  plenty  of  room  for  future  growth. 
In  the  upper  curve  of  Fig.  209  the  scale  was  purposely  selected  for 
the  first  year  so  that  the  curve  would  extend  only  about  one-third 
of  the  way  to  the  top  of  the  ruled  portion  of  the  card.  This  would 
allow  the  sales  to  be  trebled  in  volume  before  the  curve  would  extend 
over  the  top  of  the  ruled  portion  and  necessitate  a  change  in  scale 
or  a  step  upward  so  that  the  zero  line  could  no  longer  be  shown  at 
the  bottom  of  the  card.  It  is  well  to  start  all  curves  for  output  or 
sales  at  about  one-third  of  the  height  of  the  card  so  as  to  allow  plenty 
of  room  for  future  expansion.     Curves  for  expenses  per  unit,  however. 


CURVES    FOR    THE    EXECUTIVE  275 

may  be  started  well  up  on  the  card  if  there  is  any  hope  whatever  of 
reducing  the  unit  expenses  in  future  years. 

The  man  who  plots  curves  on  the  cards  described  here  keeps  a 
supply  of  the  printed  cards  in  each  of  the  two  rulings  of  seven  spaces 
high  and  ten  spaces  high.  When  starting  any  new  curves  he  uses 
w^hichever  of  the  tw^o  cards  gives  the  scale  best  suited  to  his  purpose. 
The  cost  of  carrying  two  different  kinds  of  ruled  cards  on  hand  is 
negligible  compared  with  the  great  convenience  resulting. 

The  ruling  of  the  cards  in  which  the  vertical  spaces  are  either 
i-inch  or  i-inch  high  permits  the  use  of  an  engineer's  scale  in  forti- 
eths or  sixtieths  of  an  inch,  if  it  should  ever  be  desired  to  locate  plot- 
ted points  on  the  cards  with  very  great  accuracy.  The  engineers'  scale 
in  fortieths  or  sixtieths  of  an  inch  gives  ten  divisions  to  each  space 
between  the  horizontal  lines  on  the  card  and  makes  it  possible  to  locate 
each  plotted  point  with  a  very  finely  sharpened  lead  pencil  or  a  needle. 
Practice,  however,  proves  that  there  is  no  necessity  for  using  an  en- 
gineer's scale  in  plotting  curve  points  on  the  cards  here  described. 
The  man  doing  the  plotting  learns  very  quickly  to  locate  the  points 
by  using  only  the  eye  and  a  hard  lead-pencil,  so  that  the  points  are 
practically  as  accurate  as  if  spaced  w4th  an  engineer's  scale  and  a 
needle  point.  Even  if  the  points  on  the  curve  are  not  located  quite 
so  accurately  as  they  may  be  when  a  needle  point  and  a  scale  are 
used,  it  makes  no  difference  to  the  executive  by  whom  the  curve  is 
read.  The  figures  denoting  the  value  of  each  plotted  point  are  given 
immediately  over  the  point  in  the  upper  margin.  The  executive 
reading  the  curve  does  not  have  to  refer  to  the  vertical  scale.  He 
need  only  glance  at  the  figures  above  any  point  to  learn  the  value 
for  that  point  far  more  correctly  than  would  ever  be  possible  with 
even  the  most  accurately  plotted  curve  if  the  value  of  the  point  had 
to  be  interpolated  from  the  vertical  scale  of  the  chart.  The  vertical 
scale  of  these  cards  on  which  the  figures  are  given  in  the  upper  margin 
fulfills  almost  no  purpose  except  that  of  giving  a  record  of  the  scale 
to  the  man  who  must  plot  points  in  succeeding  months,  or  that  of 
giving  the  values  of  horizontal  lines  which  are  convenient  in  locating 
high  points  or  low  points  on  any  curve. 

When  another  point  has  to  be  added  on  a  large  number  of  curves  for 
a  succeeding  month  or  week,  the  most  convenient  procedure  consists 
in  first  copying  upon  all  curve  cards,  immediately  above  the  vertical 
line  for  the  proper  month,  the  figures  from  the  typewritten  reports,  or 


276 


GRAPHIC   METHODS 


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other  sources  of  informa- 
tion. This  is  straight 
clerical  work  and  may  be 
done  with  a  pen  on  one 
card  after  another  with 
great  rapidity.  Ordi- 
nary liquid  drawing  ink  is 
the  best  for  the  figures,  as 
the  opaqueness  of  the 
drawing  ink  gives  better 
blue  prints  than  are  ob- 
tainable from  writing  ink. 
This  is  often  partly  trans- 
parent and  prints  pale 
blue  instead  of  clear 
white.  After  the  figures 
have  been  entered  on  all 
the  cards,  the  cards  are 
taken  rapidly  one  by 
one  and  a  sharp  lead- 
pencil  is  used  to  mark 
on  the  proper  vertical 
line  a  point  which,  ac- 
cording to  the  vertical 
scale,  corresponds  with 
the  newly  recorded  fig- 
ures in  the  upper  margin. 
When  all  the  curve  points 
have  been  located  by 
lead-pencil  marks  on  the 
curve  cards,  a  drawing 
pen  is  used  to  draw  the 
line  on  each  card  to  show 
the  change  that  has  oc- 
curred since  the  previous 
point  was  plotted.  As  the 
new  point  has  already 
been  indicated  in  each 
case   by   the   lead-pencil 


CURVES    FOR    THE    EXECUTIVE  277 

mark,  all  the  ink  lines  can  be  drawn  in  rapidly  with  a  draftsman's 
ruling  pen.  If  the  suggested  procedure  is  used,  the  lines  may  be  drawn 
so  rapidly  that  there  is  no  chance  for  the  ink  to  dry  on  the  pen  and  the 
ruling  operation  is  almost  continuous. 

In  Fig.  212  we  find  on  a  reduced  scale  the  same  card  that  was  pre- 
sented in  Fig.  206.  Fig.  206  was  drawn  to  full  scale  in  order  to  show 
the  true  size  of  the  figures  and  the  actual  spacing.  Fig.  212  gives  a 
better  idea  of  the  proportion  of  this  card,  and  though  of  reduced  size, 
it  nevertheless  shows  the  appearance  of  a  card  suitable  for  the  plotting 
of  records  for  one  year  by  weeks,  and  thus  requiring  fifty-two  entries 
of  figures  in  the  upper  part  of  the  card. 

In  Fig.  212  the  arrangement  to  show  the  dates  along  the  bottom  of 
the  card,  with  short  vertical  lines  dividing  the  horizontal  scale  into 
months,  is  not  put  on  to  the  card  until  the  exact  year  is  known  for  which 
the  particular  card  is  to  be  used.  Lines  dividing  the  year  into  months 
so  as  to  show  exactly  how  many  weeks  are  included  in  each  month  and 
at  just  which  portion  of  the  week  the  beginning  or  end  of  each  month 
may  occur  are  then  put  in  by  hand.  In  Fig.  212  the  card  has  been  used 
for  a  fiscal  year  beginning  August  1.  The  card  is  marked  1911, 
meaning  the  fiscal  year  ending  July  31,  1911.  By  referring  to  the 
calendar  for  the  year  1911  one  may  see  how  the  short  lines  for  months 
are  put  in.  As  the  pay  weeks  ended  on  Thursday,  there  were  only  four 
pay  weeks  ending  in  July,  but  there  were  five  pay  weeks  ending  in 
March.  March  1  came  on  Wednesday.  The  last  day  of  March  was  on 
Friday.  The  vertical  co-ordinate  lines  for  March  show  clearly  that 
there  were  five  Thursdays,  and  they  also  show  the  exact  time  relation 
of  the  Thursdays  to  the  beginning  and  to  the  end  of  the  month. 

After  the  month  scale  for  any  fiscal  year  has  been  marked  by  hand 
on  one  card,  any  office  boy  can  quickly  copy  the  scale  to  other  cards  by 
superimposing  the  first  card  on  the  next  card  and  copying  the  pen 
strokes  from  the  first  onto  the  second  card.  A  supply  of  cards  for  any 
year  can  thus  be  made  up  at  small  expense,  without  having  to  have 
cards  printed  differently  each  year  just  because  mankind  has  not  yet 
made  a  calendar  which  always  has  the  same  relation  between  days  of 
the  week  and  days  of  the  month.  The  scheme  of  indicating  the  rela- 
tion of  weeks  and  months  by  the  short  vertical  pen  marks  permits  the 
carrying  on  hand  of  a  supply  of  printed  cards  which  can  be  used  for 
absolutely  any  fiscal  year  without  danger  of  having  to  send  the  supply 
of  cards  to  the  scrap  basket,  as  calendars  are  sent  to  the  scrap  basket 


278 


GRAPHIC    METHODS 


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just  because  last  year's 
calendar  is  of  no  use 
after  December  31. 
This  assurance  of  a 
perennial  form  instead 
of  one  which  must  be 
renewed  or  replaced 
every  year  is  no  small 
advantage.  Figures 
designating  the  months 
for  any  fiscal  year  can 
be  printed  on  the  week- 
ly card  if  desired.  In 
Fig.  212  the  figures  8,  9, 
10,  etc.,  indicating  the 
months,  can  be  printed 
on  the  cards  and  thus 
leave  to  be  inserted  by 
hand  each  year  only  the 
short  vertical  markings 
indicating  the  relation 
of  the  weeks  and  the 
months. 

Fig.  213  shows  the 
weekly  curve  card 
used  in  the  records 
of  a  dairy  farm.  The 
particular  curve  shown 
is  for  a  prize  Jersey 
cow  which  was  being 
very  carefully  tested 
in  the  hope  of  break- 
ing the  world's  record 
for  milk  production. 
The  milk  production 
each  week  is  indi- 
cated here,  in  pounds, 
together  with  the  but- 
ter-fat analysis  taken 
at     various     intervals. 


CURVES    FOR    THE    EXECUTIVE 


279 


The  days  on  which  the 
butter-fat  analysis  were 
made  are  quite  accurate- 
ly indicated  by  the  dots 
on  the  butter-fat  curve. 
Figures  for  the  milk  pro- 
duction each  week  are 
given  to  hundredths  of 
a  pound  in  the  appro- 
priate column  above, 
and  the  butter-fat  anal- 
ysis is  given  to  one  one- 
hundredth  of  one  per 
cent  for  each  date  on 
which  the  analysis  was 
made.  The  grand  total 
milk  production  for  the 
year  of  the  test  is  given 
at  the  foot  of  the  col- 
umn. Note  the  diag- 
onal arrangement  of  the 
two  headings,  "Pounds  " 
and  "Per  cent  Butter 
Fat".  This  diagonal 
arrangement  is  a  con- 
venient one  as  it  is  easy 
to  read  and  refers  to 
each  of  two  columns  of 
figures,  one  column  ver- 
tical and  the  other  hori- 
zontal. 

A  card  for  each  cow 
as  indicated  above  is 
.  worth  while  in  a  modern 
dairy.  Individual  rec- 
ords are  fundamentally^ 
necessary  to  efficient 
operation.  There  is  such 
a  wide  variation  in  cows 
that  unless  they  are  care- 


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fully  watched  there 
are  certain  to  be  in 
every  herd  cows  whose 
milk  production  is  far 
below  the  average. 
Individual  records  of 
each  cow  are  now  be- 
ing kept  regularly  by 
up-to-date  dairies, 
and  any  cow  that  fails 
to  give  a  definite  mini- 
mum of  milk  with  a 
definite  per  cent  of 
butter-fat  is  sent  to 
the  butcher.  Curve 
cards  are  a  conven- 
ient means  of  record- 
ing the  output  of  each 
cow  in  such  form  that 
instant  comparison 
between  cows  is  pos- 
sible. 

In  Fig.  214  a  rec- 
ord for  one  cow  for  a 
period  of  five  years  is 
shown  on  a  4 -by- 12- 
inch  card.  As  the 
card  12  inches  long  is 
necessary  for  weekly 
records,  a  card  of  the 
same  size  can  be  used 
conveniently  to  show 
five  years  by  months 
instead  of  using  five 
separate  4-by-6-inch 
cards,  one  for  each 
year.  In  Fig.  214, 
the  figures  at  the  top 
of  the  card  show  the 


CURVES  FOR  THE  EXECUTIVE  281 

milk  production  each  month  and  the  total  milk  production  for  each 
calendar  year.  The  notes  in  the  left-hand  margin  show  the  dates  on 
which  calves  were  born. 

In  Fig.  215,  also,  curves  are  plotted  on  a  card  for  five  years  by 
months.  In  this  case  there  was  no  hope  of  getting  the  cost  per  ton 
below  50  cents,  and  the  scale  was  accordingly  so  chosen  that  it  began 
at  50  cents  instead  of  at  zero  in  order  that  fluctuations  from  month 
to  month  might  be  more  carefully  observed.  As  the  zero  line  was  not 
shown  on  the  card,  the  wavy  line  was  drawn  at  the  bottom  of  the 
ruled  portion,  indicating  clearly  to  the  reader  that  he  must  not  inter- 
pret the  curve  as  though  the  bottom  were  at  zero. 

When  using  an  arrangement  showing  five  years  by  months  on  one 
card,  considerable  mental  effort  is  necessary  to  get  a  clear  interpreta- 
tion of  the  fluctuations  in  the  curve  from  year  to  year.  In  Fig.  215 
certain  peaks  in  the  curve  appear  to  have  somewhat  similar  shape. 
Thus  the  peak  for  1908  looks  like  the  peak  for  1907  until  closer  ex- 
amination shows  clearly  that  the  low  point  for  1908  was  in  July, 
while  the  low  point  foHowing  the  peak  of  1907  came  not  in  July,  1907, 
but  in  January,  1908.  The  waves  themselves,  although  of  somewhat 
similar  shape,  have  peaks  at  entirely  different  times,  the  peak  for  1908 
being  in  February  and  the  peak  for  1907  in  April.  The  foregoing 
examples  may  serve  to  point  out  the  mental  effort  necessary  in  read- 
ing horizontally  if  the  danger  of  misinterpretation  is  to  be  avoided. 
If  the  curves  for  these  same  years  1907  and  1908  were  plotted  on 
4-by-6-inch  cards,  and  one  card  placed  above  the  other  as  in  Fig.  207, 
there  would  be  no  possibility  of  error  on  the  part  of  the  reader.  The 
eye  would  follow  the  vertical  lines  and  see  at  once  that  there  was  no 
great  similarity  in  the  two  waves.  Having  five  separate  cards  causes 
the  reader  to  take  more  time  in  handling  cards  in  order  that  he  may 
save  mental  effort  and  avoid  error  in  interpreting  the  yearly  waves. 
Having  five  years  on  one  card  saves  handling  the  cards,  but  it  takes 
more  mental  effort  to  be  accurate  in  reading  the  curve  horizontally. 
The  choice  between  five  cards  of  one  fiscal  year  each  and  one  card 
for  five  years  must  rest  with  the  judgment  or  the  habit  of  mind  of 
each  individual  person. 

It  sometimes  happens  that  the  seasonal  wave  in  a  curve  is  almost 
completely  obscured  by  the  tendency  toward  a  very  great  increase 
or  decrease  in  the  business.  Conditions  may  give  so  large  an  increase 
in  volume  of  business  in  any  one  year  as  to  more  than  offset  any  de- 


282  GRAPHIC    METHODS 

crease  due  to  a  seasonal  period  of  slackness.  The  manager  may  think, 
therefore,  that  his  business  is  not  affected  by  seasons,  when  in  reality 
the  seasonal  changes  are  very  great.  The  extent  of  these  might  be 
very  evident  if,  for  instance,  a  panic  year  should  come  along  and 
suddenly  stop  the  upward  tendencies  in  the  curve  resulting  from 
the  rapid  increase  in  the  size  of  the  business.  This  is  an  important 
point  for  any  small  business  to  watch,  for  it  may  involve  bankruptcy 
to  assume  that  the  particular  business  is  not  affected  by  slack  seasons 
of  the  year  such  as  affect  most  businesses.  Fig.  211  gives  an  example 
of  a  curve  in  which  a  large  amount  of  seasonal  fluctuation  might  be 
easily  seen  if  the  rapid  increase  in  the  business  did  not  make  the  up- 
ward trend  from  increased  sales  greater  than  the  possible  downward 
trend  due  to  seasonal  changes. 

It  is  often  necessary  to  compare  curves  for  entirely  different  things. 
For  instance,  it  is  desirable  to  compare  expenses  with  sales.  When 
sales  increase  expenses  per  unit  should  decrease,  and  vice  versa.  Tre- 
mendous saving  can  be  made  in  most  large  manufacturing  plants  by 
carefully  watching  the  curves  for  the  unit  expenses  and  the  output. 
Something  is  usually  wrong  in  any  department  in  which  expenses 
per  unit  increase  at  the  same  time  that  the  output  curve  goes  upward. 
When  the  amount  of  work  done  is  fluctuating  greatly,  as  during 
periods  of  business  depression,  the  executive  may  often  get  many  vital 
hints  for  the  operation  of  his  plant  if  he  will  simply  make  periodic 
examinations  to  see  whether  the  overhead-expense  curves  for  each 
department  react  in  the  manner  which  would  be  indicated  by  fluctua- 
tions in  the  curves  for  direct  labor  or  for  quantity  of  output. 

In  making  comparisons  between  separate  curves  there  is  a  great 
advantage  in  having  a  standard  arrangement  of  the  five-year  cards 
so  that  there  may  be  no  danger  of  comparing  two  curves  for  different 
years  when  it  is  intended  to  compare  for  the  same  year.  It  is  desirable, 
as  seen  in  Fig.  215,  that  all  five-year  cards  should  have  the  years 
arranged  by  half -decades.  One  arrangement  includes  those  years 
ending  in  one  to  five  inclusive,  and  the  other  arrangement  takes  those 
years  ending  in  six  to  ten  inclusive.  The  person  reading  the  curves 
can  then  pick  up  any  two  cards  relating  to  the  same  half-decade  and 
compare  the  curves  instantly  and  correctly,  simply  by  placing  the 
cards  so  that  the  edges  coincide.  If  this  half-decade  arrangement 
were  not  followed  there  would  be  five  different  positions  in  making 
curve  comparisons,  and  there  would  be  grave  possibility  of  frequent 


CURVES  FOR  THE  EXECUTIVE  283 

error  in  that  different  years  might  be  compared  without  the  reader's 
noticing  that  he  was  making  an  error.  In  starting  a  new  curve  on  a 
five-year  card  the  curve  should  be  started  in  the  middle  of  the  card 
if  the  first  year  plotted  happens  to  fall  in  the  middle  of  a  half -decade. 
The  half -decade  arrangement  should  be  carefully  followed  even  though 
it  does  not  leave  a  portion  of  a  card  unfilled. 

The  fine-line  curve  running  through  Fig.  215  represents  a  twelve- 
months moving  average  of  the  points  on  the  heavy  curve.  If  the 
executive  wishes  to  know  the  general  trend  of  his  costs,  he  refers  at 
once  to  this  fine  line  and  sees  what  the  cost  has  been  for  the  last  twelve 
months  for  which  costs  are  known.  In  making  up  this  moving  average 
(as  explained  in  Chapter  VI),  one  month  is  dropped  from  the  addition 
and  another  month  is  included  in  the  addition,  so  that  the  twelve 
months  added  are  always  the  most  recent  months  for  which  figures  are 
available.  Note  in  Fig.  215  the  degree  of  accuracy  used  in  recording 
the  figures  for  the  curves.  Costs  are  known  quite  accurately  in  this 
case  and  are  recorded  here  to  one  one-hundredth  of  a  cent.  The  moving- 
average  line  shown  above  is  a  much  simpler  line  than  the  curve  line,  for 
the  reason  that  the  violent  fluctuations  in  the  heavy  curve  are  largely 
eliminated  by  the  method  of  moving  averages.  The  general  rule  for 
smoothing  a  curve  is  that  the  number  of  points  included  in  the  moving 
average  should  be  the  number  ordinarily  found  in  one  complete  cycle 
or  wave  on  the  curve.  This  principle  also  was  more  fully  discussed 
in  Chapter  VI.  In  Fig.  215  the  length  of  the  wave  is  approximately 
one  year.  It  is  accordingly  good  practice  to  hc:ve  twelve  points  in- 
cluded here  in  making  up  the  moving  average,  so  as  to  give  as  smooth  a 
curve  as  possible.  If  there  had  been  a  complete  wave  or  cycle  every 
six  months  instead  of  once  a  year,  it  would  have  been  desirable  to  use 
six  points  in  the  moving  average,  rather  than  twelve  points.  The  prac- 
tice in  many  offices  is  to  use  the  last  twelve  months  in  making  up  a 
moving  average,  though  it  frequently  occurs  that  a  smoother  curve 
would  be  obtained  if  some  other  number  of  months  were  used. 

As  will  be  seen  by  reference  to  Fig.  91,  points  for  a  moving-average 
curve  are  usually  plotted  in  the  middle  of  the  horizontal  space  covered 
by  those  points  included  in  the  moving  average.  In  executive-control 
curves  such  as  are  seen  here,  it  seems  desirable  to  make  an  exception 
to  the  general  rule  and  plot  the  last  point  on  the  moving-average  curve 
so  that  it  falls  on  the  same  vertical  co-ordinate  line  as  the  last  point 
included  in  the  average.     If  the  moving-average  curve  were  made  as 


284  GRAPHIC   METHODS 

in  Fig.  91  it  would  be  following  so  far  behind  the  periodic  record  curve 
that  the  ordinary  reader  would  not  realize  that  the  moving-average 
curve  is  really  up-to-date.  For  executive  work,  the  object  of  a  moving- 
average  curve  is  not  so  much  to  get  a  smooth  curve  as  to  show  the  aver- 
age for  the  preceding  year  or  other  period  of  time  considered.  Under 
these  circumstances  it  seems  permissible  to  plot  the  moving-average 
curve  as  done  in  Fig.  215  instead  of  following  the  accepted  method 
shown  in  Fig.  91. 

In  the  last  portion  of  Chapter  VII  some  of  the  disadvantages  of  plot- 
ting curves  on  ordinary  ruled  co-ordinate  paper  were  discussed.  One  of 
these  disadvantages  is  due  to  the  great  difference  in  fluctuation  with 
curves  of  small  and  of  large  numerical  quantities  placed  near  the  bottom 
and  near  the  top  of  a  chart.  In  order  to  overcome  this  disadvantage, 
curves  are  often  plotted  on  logarithmic  paper.  It  seems  desirable  to 
point  out  that  curves  plotted  on  the  curve  cards  described  here  are 
usually  compared  so  that  the  disadvantages  commonly  found  with 
curves  plotted  on  ordinary  co-ordinate  paper  are  largely  overcome. 
If  only  single  curves  are  plotted  on  each  curve  card,  and  the  zero  line 
appears  at  the  bottom  of  each  card,  then  curves  on  different  cards  have 
approximately  the  same  percentage  scale.  If  two  curve  cards  with 
different  numerical  scales  are  compared  the  comparison  is  much  more 
accurate  than  would  be  the  case  if  the  two  curves  were  plotted  on  a 
large  sheet  of  paper  to  the  same  numerical  vertical  scale.  The  fact 
that  the  curves  are  all  put  into  the  same  size  of  space  on  the  curve  cards 
causes  them  to  have  somewhere  near  the  same  percentage  scale  of 
height,  even  though  the  actual  numerical  scales  may  be  widely  different. 
Having  all  curves  on  the  curve  cards  thus  gives  more  accuracy  and  ease 
of  reading  than  would  be  obtained  if  several  curves  were  shown  on 
large  sheets  of  arithmetically  ruled  co-ordinate  paper  with  one  curve 
above  the  other  to  the  same  scale. 

On  the  left-hand  edge  of  each  curve  card  shown  in  this  chapter  will 
be  noticed  the  word  "Authorized"  with  a  space  for  a  date  and  initials. 
When  a  new  curve  is  added  to  the  list  of  those  curves  which  are  regularly 
plotted  in  any  organization,  the  man  who  desires  to  see  the  curve  periodi- 
cally must  put  his  initials  and  the  date  of  signing  on  the  left-hand 
margin  of  the  card.  This  is  to  show  his  approval  of  the  general  form 
in  which  the  information  is  given,  and  to  authorize  the  expense  neces- 
sary in  collecting  data  and  plotting  the  curve  week  by  week  or  month 
by  month.     A  definite  authorization,  by  which  some  one  must  sign  his 


CURVES  FOR  THE  EXECUTIVE  285 

initials  in  the  manner  described,  assists  greatly  in  preventing  unneces- 
sary clerical  work,  as  it  eliminates  any  curves  which  are  not  used 
somewhere  in  the  organization.  The  man  who  approves  the  curve 
can  be  told  just  about  what  it  costs  to  plot  each  curve.  For  instance, 
if  three  thousand  dollars  a  year  is  expended  for  the  labor,  materials, 
etc.,  necessary  in  plotting  all  the  curves  in  an  organization,  and  there 
are  three  thousand  curves  kept  regularly,  it  can  be  seen  that  the  ex- 
pense per  curve  per  year  will  be  about  one  dollar.  Therefore,  if  the 
man  should  wish  one  hundred  curves  plotted  for  different  data  relating 
to  his  department,  he  would  be  approving  an  expenditure  of  about 
one  hundred  dollars  per  year. 

At  odd  times  before  the  end  of  any  year  the  person  who  does  the 
curve  plotting  should  begin  to  get  titles  and  scales  in  place  upon  the 
new  cards,  which  will  be  necessary  at  the  end  of  the  year  when  the  cur- 
rent curves  have  reached  the  right-hand  edge  of  the  cards.  As  most 
curves  continue  on  the  same  basis  as  before,  the  man  who  has  charge 
of  the  plotting  would  take  the  new  cards  to  those  different  men  who  had 
approved  the  curves  in  the  preceding  year.  If,  during  that  year,  any 
change  in  departmental  organization  had  occurred  which  would  affect 
the  manner  of  plotting  a  curve  or  the  facts  which  should  be  shown  in 
any  curve,  the  change  would  automatically  be  brought  to  light  by  the 
man  who  must  authorize  the  continuance  of  the  curve.  In  large  cor- 
porations, department  heads  and  officials  change  so  rapidly  that  con- 
tinual vigilance  is  necessary  to  weed  out  those  records  and  clerical 
procedures  which  are  no  longer  of  any  use.  The  authorization  plan 
here  outlined,  if  any  man  leaves  a  corporation,  would  automatically 
give  his  successor  an  opportunity  to  consider  how  much  of  the  curve 
plotting  should  be  continued  on  the  basis  formerly  used.  There  is 
always  a  great  personal  difference  in  the  manner  in  which  executives 
desire  reports  prepared.  The  authorizing  of  curves  periodically  gives 
each  executive  an  opportunity  to  think  the  matter  over  and  to  have 
data  prepared  in  the  manner  which  is  most  effective  for  his  individual 
use.  In  most  organizations  the  president  or  the  general  manager  would 
be  likely  to  have  certain  standard  ways  of  assembling  data  and  plotting 
curves,  since  the  chief  executive  oflScer  must  usually  refer  at  some  time 
to  each  of  the  records  of  the  different  departments.  The  standards 
of  the  chief  executive  would  thus  tend  to  prevent  any  freak  methods 
being  introduced  into  the  general  curve-plotting  scheme  by  any  depart- 
ment head  further  down  the  fine. 


286 


GRAPHIC    METHODS 


ac>7ft 


^isA 


SJSu. 


c.  •     hVft        ^    ft.         0    o  ^    •  -C3  -V-     ft  .<=>V    "^ 


;^>^^..Aq_  juj^slk 


>>n.  Vo>./Juai,» ^tr>-«J." 


Each  curve  plotted  regularly  is  assigned  a  serial  number  for  con- 
venient identification.  This  serial  number  remains  the  same  year  after 
year,  even  though  changes  are  made  in  the  manner  of  assembling  data 
or  in  any  other  minor  details  affecting  the  curve.  The  serial  number 
is  placed  at  the  upper  left-hand  corner  of  the  card,  where  it  can  easily 
be  seen  when  the  cards  are  filed  in  card-index  filing  cabinets.  The  cards 
are  identified  by  the  number  and  year,  as  may  be  seen  in  Fig.  211  where 
the  three  cards  are  igiJ  fm  IqiL  When  two  curves  appear  on  the  same 
card,  as  in  Fig.  215,  they  may  be  identified  by  the  letters  "A",  "B", 

"C",  etc.,  placed  on 
the  chart  near  each 
curve,  and  any  refer- 
ence to  the  several 
curves  may  be  made 
as4323A-1910,4323B 
-1910,  etc.  When 
five  years  are  placed 
on  one  card  the  last 
year  given  is  marked 
in  the  upper  left- 
hand  corner  of  the 
card,  as  in  Fig.  215, 
to  identify  the  card 
and  show  that  it 
represents  all  the 
data  for  the  half- 
decade  ending  in 
that  year. 


A«^   /'-»Jt,^A<».^..^j>l^ 


^ 


£l.aS«A 


^O^Cru«A«_. 


f^^^^oSJLfK/^Jn^^^^ 


^^..IL^ 


j^  CiL.^,^  ft«6^i»^t/t- -^A^JW,  .^  (lAxx^^^:^/ 


:xs 


X.\-  t^J^JiXf,  ^<^..^i. 


s 


/^^--ovdH . 


*lJb- 


VLayktJ>.X/t^    X.^.^l^-  »M.     IL.      ?s»S.«^ ^^Wr^^tA<r>vJ   l6^ 


Fig.  2 1 6.  Each  Curve  Card  Plotted  Periodically  Has  a 
Serial  Number.  A  4-inch  by  6-inch  Record  Card  is 
Filed  by  the  Curve  Serial  Number  to  Give  the  Com- 
plete Information  Necessary  so  that  Anyone  May 
Know  How  to  Collect  the  Data  and  Plot  the  Curve. 
The  Card,  Shown  Above,  Refers  to  Curve  2678  Shown 
for  Three  Years  in  Fig.  207  and  in  Fig.  208 


It  is  not  feasible  or  desirable  to  place  on  each  curve  card  a  title  so 
complete  that  it  gives  all  the  information  concerning  the  source  of  the 
data  used  in  plotting  the  curve.  It  is  better  to  use  a  fairly  short  title, 
and  then  have  all  supplementary  information  given  on  a  separate  card 
to  which  reference,  if  necessary,  can  easily  be  made.  Fig.  216  shows  a 
4-by-6-inch  card  such  as  is  used  in  conjunction  with  each  curve  card 
regularly  plotted.  The  number  on  this  card  corresponds  with  the  serial 
number  on  the  curve  card  as  will  be  seen  by  referring  to  Fig.  205  and 
Fig.  207.  If  two  or  more  curves  appear  on  the  curve  card,  a  card  like 
that  in  Fig.  216  would  have  subheadings  such  as  2678A,  2678B,  etc., 
all  shown  on  the  same  card  No.  2678.     It  will  be  seen  that  the  informa- 


CURVES  FOR  THE  EXECUTIVE  287 

tion  given  on  the  card  in  Fig.  216  is  much  too  lengthy  to  be  included 
as  a  portion  of  the  title  of  any  curve  card.  The  information  on  the 
record  card  is  so  specific  that  a  new  man  in  an  organization  should  be 
able  to  follow  the  card  instructions  and  assemble  all  the  data  necessary 
to  plot  each  curve  in  the  whole  set. 

Information  cards  such  as  are  shown  in  Fig.  216  can  sometimes  be 
simplified  by  expressing  the  information  as  a  formula.  Curve  numbers 
used  in  a  formula  may  greatly  simplify  the  method  of  expressing  the 
fact  that  several  sets  of  data  must  be  added  and  one  total  divided  into 
another  total  to  obtain  a  desired  ratio.  Though  information  cards  like 
that  depicted  in  Fig.  216  are  used  principally  by  the  man  who  plots 
the  curves,  they  are  filed  in  such  convenient  location  that  they  may  be 
referred  to  by  any  executive  who  wishes  to  know  the  source  of  the  data 
plotted  on  any  curve  card,  or  who  wishes  to  see  just  what  figures  are 
included  and  w^hat  are  excluded  in  making  up  any  grand  totals.  The 
use  of  the  serial  numbered  information  card  gives  full  information  in 
condensed  and  easily  accessible  form. 


Chapter  XIV 
RECORDS  FOR  THE  EXECUTIVE 

A  GOOD  executive  has  been  described  as  a  man  who  decides 
quickly  and  who  is  sometimes  right.  Probably  ninety  per 
cent  of  the  answers  "Yes"  or  "No"  given  by  a  business 
man  are  based  on  opinion  rather  than  on  fact.  The  trouble  is  that 
the  average  executive  cannot  obtain  and  analyze  facts  quickly  enough 
to  base  his  decision  on  them.  He  is  forced  to  decide  quickly  and  his 
one  hope  is  that  he  will  guess  "right". 

The  problems  confronting  the  executives  have  grown,  in  the  last 
few  years,  to  such  an  extent  in  volume  and  in  complexity  that  it  is 
increasingly  diflScult  to  find  men  with  endurance  and  capacity  great 
enough  to  match  the  jobs.  The  executives  of  our  corporations,  the  men 
who  are  mayors  of  our  cities,  and  the  men  in  active  charge  of  the  govern- 
ment of  our  country  are,  without  exception,  the  hardest  worked  men  in 
the  world.  The  stoker  heaving  coal  into  the  furnaces  of  an  express 
steamer  has  a  better  chance  for  long  life  than  the  man  who  accepts  the 
presidency  of  even  our  best  managed  railroads  and  industrial  corpora- 
tions. The  stoker  can  at  least  sleep  soundly  at  the  end  of  his  day's 
work.  The  railroad  president  is  likely  to  be  kept  awake  wondering 
whether  his  guess  was  a  good  one,  whether  his  decision  was  "right". 

The  men  now  steering  the  courses  of  our  big  corporations  are  men 
who  have  come  up  the  line,  step  by  step,  through  each  department. 
They  know  accurately  the  relation  of  every  department  to  every  other 
department  in  their  own  company.  They  have  available,  also,  a  tre- 
mendous fund  of  information  as  to  what  has  been  accomplished  by  their 
competitors.  The  present  executives  of  corporations  are  fortunate, 
in  that  they  have  seen,  in  their  own  business  experience,  each  of  the 
steps  toward  the  greater  division  of  labor  and  the  consolidation  of 
executive  control  which  have  done  so  much  to  make  economic  produc- 
tion possible  by  large-scale  production. 

288 


RECORDS  FOR  THE  EXECUTIVE  289 

The  present  executives  are  extremely  fortunate  in  that  they  had 
an  opportunity  to  develop  themselves  at  the  same  time  that  their 
jobs  grew  bigger.  What  are  we  going  to  do  ten  years  hence,  when  execu- 
tives who  have  had  such  thorough  training  have  all  retired  or  have  been 
killed  off  by  the  strain  of  the  job?  Where  shall  we  find  men  with  broad 
enough  knowledge  and  experience  to  decide,  instantly  and  correctly, 
each  problem  placed  before  them? 

The  answer  is  that  the  executive  of  the  future  will  be  forced  to 
depend  on  the  analysis  of  facts  which  have  been  collected  and  arranged 
for  his  instantaneous  and  continuous  use.  The  executive  of  the  future 
will  decide  quickly,  and  he  will  be  more  than  "sometimes"  right,  be- 
cause he  will  base  his  decisions  on  the  analysis  of  actual  facts.  His 
value  as  an  executive  will  depend  chiefly  upon  his  powers  of  accurate 
analysis. 

Corporation  directors  are  changing  rapidly  these  days.  Suppose 
a  new  director  were  to  come  into  your  corporation,  what  could  you  show 
him  of  the  history  and  present  standing  of  your  business  that  would 
permit  him  to  give  an  intelligent  director's  vote  within  a  year  of  his 
election  to  the  board? 

It  is  perfectly  feasible  to  focus  a  whole  business  into  records  so 
simple  that  a  trained  man  could  see,  in  half  a  day,  all  the  important 
tendencies  w^ell  enough  to  give  an  intelligent  director's  vote.  This, 
too,  without  a  spoken  word  of  explanation  from  anyone.  The  records 
themselves  could  tell  the  complete  story  in  every  detail  if  placed  in 
proper  graphic  form.  It  is  the  purpose  of  this  chapter  to  show  how 
such  a  thing  may  be  done. 

Fig.  217  shows  a  standard  4-by-6-inch  filing  case  used  to  file  curve 
cards  and  information  cards.  The  right-hand  drawer  shows  the  4-by- 
6-inch  cards  filed  with  appropriate  guide  cards.  In  this  particular 
case,  the  guides  give  the  names  of  branch  houses  by  cities.  The  left- 
hand  drawer  shows  the  4-by-12-inch  cards  filed  according  to  the  loca- 
tion of  factories.  As  factory  pajTolls  must  be  watched  closely,  weekly 
records  of  the  payrolls  were  kept  for  this  corporation,  though  monthly 
curves  were  found  to  be  sufficient  for  the  sales.  There  is  no  difficulty 
in  filing  the  4-by-12-inch  cards  in  a  standard  4-by-6-inch  filing  cabinet. 
The  follow-up  block  in  the  drawer  is  placed  12  inches  from  the  end  of 
the  drawer,  then  the  cards  are  filed  lengthwise  with  a  sufficient  quantity 
of  blank  cards  at  the  back  to  keep  all  the  cards  in  an  upright  position. 
Of  course  a  special  filing  cabinet  12  inches  wide  can  be  made  if  desired. 


290  GRAPHIC    METHODS 

but  it  is  not  really  necessary.  In  a  cabinet  like  that  shown  in  Fig.  217, 
the  original  curve  cards  would  ordinarily  be  filed  behind  the  guide  cards 
showing  the  factory  or  selling-house  locations,  or  behind  guide  cards 
showing  the  names  of  departments  in  any  large  business.  All  the  cards 
for  succeeding  years  would  be  filed  behind  the  proper  guide  cards,  with 
the  curve  card  for  the  earlier  year  at  the  front.  Having  the  card  for 
the  earlier  year  at  the  front  instead  of  at  the  back  permits  comparison 
of  curves  for  different  years  with  a  very  slight  lifting  of  the  cards, 
and  without  any  danger  of  the  cards  being  put  back  in  the  drawer  in 
mixed  order. 

Information  cards  like  those  shown  in  Fig.  216  would  be  filed  in 
the  same  filing  cabinet.  These  4-by-6-inch  information  cards  are  filed 
by  curve  serial  numbers,  with  appropriate  numbered  guide  cards  so 
that  any  information  card  may  be  quickly  located  by  its  serial  number., 
As  the  numbered  information  cards  are  needed  only  for  occasional 
reference,  they  can  be  put  in  the  back  portion  of  a  file  drawer,  leaving 
the  front  portion  of  the  drawer  available  for  the  curve  cards  more  fre- 
quently needed. 

In  checking  up  the  condition  of  his  business,  the  executive  usually 
considers  it  department  by  department.  For  this  reason  the  original 
curve  cards  should  be  filed  by  departments  so  that  the  complete  history 
of  any  department  may  be  had  from  the  cards  behind  the  guide  card  for 
that  department.  A  large  portion  of  the  executive's  work,  however,  in- 
volves the  study  of  his  general  business  not  by  departments  but  by 
functions.  For  instance,  the  executive  may  wish  to  know  how  many 
employees  he  has  in  his  whole  business,  and  how  many  employees  there 
are  in  each  department,  if  he  is  considering  the  departmental  increases 
or  decreases  which  affect  the  total  payroll.  It  is  therefore  desirable 
that  the  executive  should  have  available  for  instant  reference  a  cross- 
index  of  information  which  will  show  his  whole  business  by  function 
instead  of  by  department.  Such  a  cross-index  can  easily  be  provided, 
when  curve  cards  are  used,  by  taking  a  blue  print  of  each  curve  card 
and  then  filing  the  blue  print  by  function,  instead  of  by  department. 
In  such  an  arrangement,  there  would  be  a  complete  set  of  guide  cards 
giving  different  headings,  such  as  "Number  of  Employees",  "Total 
Sales",  "Total  Expenses",  etc.,  with  guide  cards  having  suitable  sub- 
headings placed  behind  each  one  of  the  main  guide  cards.  A  blue 
print  of  the  curve  show  ing  the  total  number  of  employees  in  the  corpora- 
tion would  be  filed  at  the  front  of  the  division  for  employees.     Back  of 


RECORDS  FOR  THE  EXECUTIVE 


291 


this  total  card  would  be  filed  blue  prints  showing  the  employees  in  each 
department  of  the  whole  plant.  Thus,  if  a  total  card  at  the  front 
showed  that  the  employees  were  increasing,  the  manager  could  refer 
to  each  one  of  the  department  cards  filed  immediately  back  of  the  total 
card  to  see  in  just  which  departments  there  had  been  an  increase  during 
the  last  month,  and  in  which  department  there  had  been  a  decrease. 


Fig.  217.  A  Standard  4-inch  by  6-inch  Filing  Case  Is  Used  for  the  Curve  Cards» 
Cards  Twelve  Inches  Long  Can  Be  Filed  Lengthwise  in  a  Drawer  without  In- 
convenience 

Guide  cards  separate  the  curve  cards  by  departments.  If  desired,  blue  prints  can  be  made  from  each  curve 
card  and  the  bhie  prints  filed  by  expense-account  numbers,  as  a  cross-index  of  the  data  on  the  white 
cards  which  are  filed  by  departments 

In  a  similar  manner,  the  blue  print  showing  total  expenses  would  have 
filed  back  of  it  cards  showing  the  detailed  expenses  by  departments 
or  by  account  numbers.  If  expenses  had  increased  the  manager  could 
refer  to  the  departmental  or  account-number  cards  and  see  just  which 
departments  or  accounts  were  responsible  for  an  increase  or  decrease 
in  the  curve  giving  the  total.  The  cards  in  a  large  business  would 
be  filed  by  expense-account  numbers,  with  the  total  card  referring  to 
any  expense  account  for  the  whole  business  filed  at  the  front  of  each 
group  of  cards  giving  the  figures  for  that  expense  account  by  depart- 
ments.    Thus,  in  a  manufacturing  plant,  the  card  showing  the  loss 


292  GRAPHIC    METHODS 

from  spoiled  work  as  a  percentage  of  the  total  payroll  could  have  filed 
back  of  it  cards  showing  the  percentage  loss  in  each  department.  If 
the  spoiled-work  curve  for  the  whole  business  should  go  up  in  any  month, 
the  manager  could  see  instantly  in  which  departments  the  percentage 
of  loss  had  increased  and  in  which  the  percentage  had  decreased.  Let- 
ters could  be  sent  to  the  foremen  of  the  departments  having  bad  records, 
calling  their  attention  to  the  bad  showing  made. 

The  cross-index  of  curves,  obtained  by  filing  the  cards  according  to 
function  or  by  expense-account  number  instead  of  by  department,  is 
of  tremendous  importance  to  the  busy  executive.  This  feature  alone 
may  save  a  large  amount  of  his  time  by  making  necessary  information 
more  accessible,  and  by  affording  information  which  may  show  leaks 
in  his  business  that  he  would  otherwise  never  know  to  exist.  In  a 
business  of  any  size  the  cost  of  making  one  blue  print  each  month  from 
each  original  curve  card  is  almost  insignificant.  The  guide  cards 
showing  functions  or  account  numbers  remain  useful  year  after  year,  and 
it  is  necessary  only  to  discard  a  blue  print  for  each  card  each  month  and 
to  substitute  the  latest  blue  print  made  from  the  original  curve  card 
after  a  new  point  has  been  added.  Having  the  original  cards  filed 
by  departments  and  the  blue  prints  filed  by  function  or  account  number, 
the  manager  may  instantly  consider  his  business  from  whichever  point 
of  view  he  desires.  He  may  study  the  whole  operation  of  a  given 
department,  or  he  may  study  one  function  or  expense  account  in  its 
effect  upon  his  business  as  a  whole. 

Practically  every  company  which  does  an  annual  business  of 
$1,000,000  or  more  would  find  it  a  paying  proposition  to  have  a  room 
reserved  in  the  office  as  a  general  record  or  information  department 
regarding  all  the  facts  of  the  business.  Though  such  a  room  might 
be  combined  with  a  technical  library  for  books  relating  to  the  particular 
art  or  industry  in  which  the  company  finds  its  field  of  operation,  it  is 
advisable  to  have  the  amount  of  furnishings  in  the  room  limited  so 
that  there  may  be  no  likelihood  of  valuable  confidential  papers  being 
lost  or  misplaced.  Such  a  room  really  needs  to  have  no  more  furniture 
than  filing  cases  like  those  shown  in  Fig.  217,  a  large  table,  and  a  draw- 
ing table  or  a  flat  desk  for  the  man  who  plots  curves. 

It  would  be  the  function  of  a  man  having  an  office  like  that  described 
to  collect  for  the  business  all  the  data  and  facts  which  would  be  of  any 
assistance  to  the  executive,  the  officers,  or  the  department  heads. 
Most  of  his  work  would  relate,  of  course,  to  getting  data  and  plotting 


RECORDS  FOR  THE  EXECUTIVE  293 

curves  for  all  the  operating  reports  of  different  departments  of  the  busi- 
ness. The  operating  reports  regularly  furnished  by  the  accounting 
departments  of  the  business  would  be  gone  through  carefully,  and 
figures  transcribed  from  these  reports  to  the  curve  cards  mentioned 
previously.  There  could  also  be  in  the  record  room  a  series  of  maps, 
large  wall  charts  in  the  form  of  curves,  and  perhaps  loose-leaf  books 
or  large  vertical  card  files  for  cumulative  curves  such  as  are  shown  in 
Fig.  134.  Since  the  information  contained  in  this  room  is  practically 
a  history  of  every  phase  of  the  business,  it  would  be  desirable  to  have 
the  room  enclosed  with  fire-proof  walls  and  fire-proof  doors  and  equip- 
ped with  fire-proof  file  cases  and  furniture  so  that  the  destruction  of 
the  records  by  fire  would  be  absolutely  impossible.  As  good  light  is 
essential  in  such  a  room,  large  windows  are  necessary.  The  windows 
can  ordinarily  be  sufficiently  protected  against  fire  by  using  polished 
plate  glass  reinforced  with  wire  to  prevent  breaking  of  the  glass  from 
fire  in  adjoining  buildings. 

The  title  given  the  man  who  does  the  work  described  is  really  not 
important.  Ordinarily,  in  a  large  corporation,  he  would  be  ranked  as 
assistant  to  the  president,  as  he  should  report  only  to  the  chief  executive 
officer  in  the  particular  office  in  which  he  is  located.  He  could,  if 
desired,  be  given  the  title  of  chief  of  the  record  department,  or,  in  a 
larger  business  where  much  specialized  information  is  sought  from 
outside  sources,  the  title  of  "statistician"  might  be  justified.  In  the 
work  of  most  corporations  it  would  soon  be  found  desirable  to  have  a 
man  of  the  type  described  collect  and  record,  for  convenient  use,  data 
from  sources  entirely  outside  of  the  business  itself.  Most  companies 
have  to  buy  large  quantities  of  raw  material  which  fluctuates  greatly 
in  price.  To  assist  in  making  decisions  relating  to  purchases,  it  would 
usually  be  found  desirable  to  have  curves  plotted  for  the  chief  materials 
entering  into  the  finished  product,  such  as  pig  iron,  copper,  tin,  zinc, 
cotton,  lumber,  coal,  etc.  Very  desirable  information  could  also  be 
obtained  concerning  the  business  conditions  of  the  country  as  a  whole. 
Since  practically  every  business  is  affected  by  the  general  waves  of 
financial  prosperity  and  depression,  a  good  man  in  this  position  could 
be  of  great  assistance  to  the  chief  executive,  by  carefully  studying 
some  series  of  curves  (which  might,  after  long  experience,  prove  to  be 
the  best  barometer  available)  to  indicate  changes  for  better  or  worse 
in  the  general  financial  conditions  affecting  the  particular  business  in 
question. 


294  GRAPHIC    METHODS 

In  a  business  of  ordinary  size,  the  yearly  outlay  for  an  office  like 
that  described  and  a  man  to  run  it  would  be  comparatively  small.  It 
would  probably  be  best  to  get  a  young  man  graduated  within  a  few 
years  from  one  of  the  technical  schools,  or  from  one  of  the  schools  of 
business  administration  now  established  as  separate  departments  in 
several  of  the  large  universities.  If  a  man  of  the  right  type  were  told 
that  he  would  report  directly  to  the  chief  executive,  and  that  he  would 
have  a  confidential  position  with  complete  access  to  the  records  of  every 
department  of  the  whole  business  including  both  manufacturing  and 
selling,  he  would  be  quite  willing  to  start  the  work  at  a  reasonable 
salary,  knowing  full  well  that  the  opportunities  given  would  soon  per- 
mit him  to  demonstrate  his  ability.  A  recent  college  graduate  could 
be  obtained  for  $20  or  $25  per  week,  as  he  would  see  for  himself  that 
there  would  be  chances  for  him  to  make  himself  worth  much  more  inside 
of  the  first  year  or  so. 

A  man  starting  a  record  department  of  the  type  described  would 
at  first  find  his  chief  work  in  getting  records  for  a  series  of  years  so 
that  comparisons  would  be  possible.  In  most  corporations  it  is  extreme- 
ly difficult  to  get  any  kind  of  good  records  further  than  two  years  back, 
because  of  constant  changes  in  personnel  and  changes  in  accounting 
systems  without  any  reliable  notes  to  tell  just  what  these  changes  were 
and  when  they  were  made.  In  large  manufacturing  companies,  sub- 
divisions and  changes  in  the  expense  accounts  are  likely  to  occur  as 
new  departments  are  added  or  as  new  men  of  different  training  in  ac- 
counting come  into  control  of  the  accounting  procedure  of  the  company. 
After  the  back  records  have  been  fairly  well  tabulated  and  plotted  in 
the  form  of  curves,  the  work  of  keeping  the  curves  up  to  date  would 
be  comparatively  simple.  One  man  can  add  one  more  point  monthly  to 
several  thousand  different  curves,  and  do  also  a  certain  amount  of 
the  clerical  work  involved  in  making  up  ratios,  grand  totals,  etc.  If 
a  record  file  of  curves  like  that  shown  in  Fig.  217  is  once  made  thorough- 
ly up  to  date,  for  any  business,  it  is  easy  to  keep  it  up  to  date  with  only 
routine  work  such  as  any  man  of  even  ordinary  mental  caliber  can  do. 
Information  cards  4-by-6-inch,  such  as  are  shown  in  Fig.  216,  explain 
every  step  of  the  work  required  in  plotting  any  curve,  and  even  a  new 
man  just  out  of  college  would  be  able  to  follow  the  instructions  well 
enough  to  take  charge  of  a  record  system  which  some  one  else  started. 
Thus,  if  it  is  desired  after  a  year  or  two  to  promote  a  man  who  has  built 
up  a  record  system  of  this  kind,  it  would  be  quite  easy  to  have  him  break 


RECORDS  FOR  THE  EXECUTIVE  295 

in  a  successor  so  that  there  would  be  no  change  in  the  methods  of  col- 
lecting data  and  plotting  curves.  This  possibility  of  taking  on  a  new 
college  graduate  every  few  years  permits  having  an  excellent  record 
department,  even  for  a  small-size  business  in  which  it  would  be  thought 
undesirable  to  spend  more  than  $3,000  or  $4,000  a  year  to  cover  the 
total  yearly  departmental  cost. 

It  should  be  a  strict  rule  for  a  record  department  of  the  type  de- 
scribed that  no  original  papers  shall  be  taken  from  the  room.  The  rec- 
ord department  should  be  in  a  quiet  place  to  which  the  president  or 
any  other  oflScial  may  retreat  to  get  completely  away  from  the  distrac- 
tions which  are  common  in  his  own  office  because  of  the  telephone  and 
constant  visitors.  In  the  record  room  the  executive  would  be  free  to 
concentrate  his  whole  attention  on  the  records  of  what  his  business 
has  been  doing  in  the  last  weeks  or  months,  so  that  he  may  be  able  to 
formulate  plans  for  the  future.  Though  the  arrangement  of  the  files 
in  the  record  room  would  be  well  known  to  the  executive,  so  that  he 
could  lay  his  fingers  instantly  on  any  desired  curve  or  other  record, 
the  chief  of  the  record  department  would  be  at  hand  most  of  the  time 
so  the  executive  could  send  word  ahead  to  have  certain  curves  or  other 
records  laid  out  for  instant  reference  when  he  arrived.  To  save  time 
the  executive  should  not  be  required  to  put  back  into  the  card  files 
the  curve  cards  which  he  has  taken  from  any  file  drawer.  By  using  a 
large  table  the  executive  could  simply  push  to  the  other  side  of  the 
table  any  cards  which  he  may  have  laid  out  for  careful  comparison. 
The  man  who  has  charge  of  the  room  can  later  put  the  cards  back  in 
the  files.  There  is  an  advantage  in  having  one  man  put  all  the  cards 
back  in  the  files,  as  in  this  w^ay  there  is  less  chance  of  the  cards  being 
misplaced  in  the  file  than  if  several  different  executive  officers  were  to 
use  the  cards  and  themselves  put  the  cards  back.  It  should  be  stated 
here  that  in  the  ordinary  use  of  curve  files  such  as  are  shown  in  Fig.  217 
an  executive  w  ould  not  need  to  remove  the  cards  from  the  drawer.  He 
would  simply  turn  the  cards  over  one  at  a  time,  raising  any  card  of 
special  interest  about  three  inches  to  look  at  it,  but  not  removing  it 
sufficiently  to  cause  any  danger  of  restoring  the  card  in  a  wrong  position. 
It  is  only  when  cards  for  a  series  of  years  are  taken  out  and  laid  down  for 
comparison  with  some  other  series  of  cards  that  there  is  any  necessity 
for  removing  the  cards  from  the  drawer. 

The  Westinghouse  Electric  and  Manufacturing  Company  of  Pitts- 
burgh regularly  plot  about  four  thousand  curves  which  record  the 


296  GRAPHIC    METHODS 

activities  of  all  departments  of  the  business.  The  majority  of  the  curves 
have  one  more  point  added  each  month,  but  some  of  the  curves  are 
on  a  weekly  basis.  Day  and  Zimmermann,  of  Philadelphia,  are  plotting 
a  total  of  about  eight  thousand  curves,  most  of  the  curves  on  a 
cumulative  basis  somewhat  as  shown  in  Fig.  134.  In  order  to  allow 
space  enough  for  a  cumulative  curve  (which  naturally  takes  up  more 
room  than  a  curve  plotted  on  a  non-cumulative  basis),  the  curves  are 
plotted  on  cards  Sj/^  inches  by  11  inches,  and  these  cards  are  filed  ver- 
tically in  a  tray  desk  so  that  a  man  sitting  at  the  desk  can  instantly 
lay  his  hand  on  the  proper  card  for  any  one  of  the  eight  thousand  curves. 
Guide  cards  are  of  course  used  to  make  card  location  easier.  To  pre- 
vent cards  being  replaced  at  some  wrong  position  in  the  file,  Day 
and  Zimmermann  have  worked  out  the  clever  scheme  of  notching  in  a 
similar  manner  the  tops  of  all  cards  which  are  filed  in  any  one  division 
of  the  file.  When  cards  are  filed  one  after  another  the  notches  of  indi- 
vidual cards  form  a  groove  in  the  group  of  cards.  If  any  card  should 
be  filed  out  of  place  it  would  break  the  continuity  of  the  groove  and 
would  instantly  be  noticed.  In  using  the  notched-card  scheme  two 
notches  may,  if  desired,  be  placed  in  the  top  of  each  card,  thus  permit- 
ting many  more  group  combinations  than  would  be  possible  if  only  one 
notch  were  used.  The  notches  may  be  cut  with  a  special  instrument  of 
rather  simple  construction  so  as  to  insure  their  uniform  spacing  right 
or  left  from  the  upper  corners  of  the  card.  A  notch  in  the  form  of  a 
segment  of  a  circle  is  the  most  satisfactory. 

In  order  to  keep  the  general  rule  that  original  curve  cards  shall 
not  be  taken  out  of  the  record  room,  it  is  well  to  provide  means  by 
which  blue  prints  can  be  made  quickly  from  any  curve  card.  In  a 
business  of  reasonable  size,  blue  prints  may  easily  be  made  with  a 
small-size  printing  frame  and  sunlight  printing,  if  the  record  room  is 
located  on  the  southern  side  of  the  building  where  there  is  sunlight  most 
of  the  time.  In  large  businesses  electric  blue-printing  machines  are  a 
part  of  the  regular  equipment  of  the  drafting  office.  If  the  drafting 
office  is  not  near  the  record  room,  however,  it  may  be  well  to  equip  the 
record  room  with  an  electric  blue-printing  machine  and  a  small  washing 
tank,  so  that  blue  prints  of  each  card  may  be  made  without  the  neces- 
sity of  taking  confidential  record  cards  out  of  the  room.  Photographic 
processes  for  copying  records  have  recently  been  much  improved.  A 
machine  called  the  photostat  makes  black  and  white  copies  quickly 
without  the  expense  of  glass  negatives.     With  a  blue-print  machine  or 


RECORDS  FOR  THE  EXECUTIVE  297 

a  photostat  in  the  record  room,  it  would  be  a  very  simple  matter  to 
copy  periodically  the  complete  current  set  of  curves  so  that  the  cross - 
index  of  cards  by  function  or  account  may  be  provided  for  the  execu- 
tive, as  described  in  the  preceding  paragraphs. 

The  plan  suggested  for  a  record  department  sounds  much  more  com- 
plex than  it  really  is.  In  considering  the  space  and  expense  necessary 
for  such  a  department  it  must  be  borne  in  mind  that  the  time  of  the  chief 
executive  of  a  modern  corporation  is  of  a  great  value — almost  beyond 
computation.  The  value  of  the  president's  time  in  a  large  corporation 
cannot  be  figured  out  on  the  basis  of  his  salary,  for  it  is  certainly  true 
that  the  executives  of  large  corporations  receive  salaries  much  less 
than  the  value  of  their  services  to  their  corporation.  A  single  "yes" 
or  "no"  decision  of  the  corporation  executive  usually  involves  a  gain  or 
loss  in  the  earnings  of  the  corporation  greater  than  the  executive's 
salary  for  a  whole  year.  Anything  that  can  be  done  to  give  the  presi- 
dent and  the  other  executives  better  and  more  quickly  available  in- 
formation on  which  to  base  decisions  is  justifiable  and  should  be  in- 
stalled practically  without  regard  to  cost. 

In  a  large  office  it  will  be  found  desirable  to  give  a  number  of 
department  heads  access  to  the  record  room.  As  no  one  would  ever  be 
admitted  to  this  room  except  the  chief  executive,  and  department  heads 
who  were  given  written  permission  by  the  chief  executive,  there  would  be 
no  danger  of  confidential  information  coming  into  the  hands  of  outside 
parties.  As  it  may  not  be  desirable  to  have  department  heads  in  a 
business  know  anything  about  the  finances  of  the  company  as  a  whole, 
or  anything  regarding  the  records  of  departments  other  than  their 
own,  it  may  be  best  to  have  the  curve  cards  filed  in  several  drawers  with 
a  separate  drawer  for  the  cards  relating  to  the  work  of  each  department 
head.  If  the  drawers  are  equipped  with  spring  locks,  each  department 
head  could  have  a  key  to  his  own  drawer,  yet  it  would  be  impossible 
for  him  to  go  through  the  records  of  departments  other  than  his  own. 
The  chief  executive  would,  of  course,  have  a  master  key  to  all  the  draw- 
ers, so  that  he  could  compare  the  records  of  one  department  with  the 
records  of  any  other  department  whenever  he  desired.  The  presence  of 
the  man  in  charge  of  the  record  department  would  in  itself  tend  to 
keep  minor  officials  from  going  through  the  cards  relating  to  bank 
deposits,  earnings,  etc.,  for  the  corporation  as  a  whole.  There  would 
necessarily  be  times  when  the  head  of  the  information  department  would 
not  be  in  the  room  while  minor  ofiicials  were  there,  and  the  expedient 


298  GRAPHIC    METHODS 

of  locking  up  the  summarized  control  curves  for  the  whole  corporation 
is  therefore  mentioned  here  as  a  possible  safeguard. 

Directors  and  executives  change  quite  frequently  in  large  corpora- 
tions. When  a  new  man  comes  into  a  corporation  as  an  executive  or  a 
director,  the  value  of  his  service  to  the  corporation  is  at  first  practically 
nothing,  and  he  may  even  for  a  while  be  considered  a  handicap  to  the 
corporation  in  that  it  is  necessary  for  men  who  have  been  associated 
longer  with  the  corporation  to  spend  a  great  deal  of  their  time  in  explain- 
ing to  the  new  member  the  facts  relating  to  the  various  departments  and 
to  the  present  scope  of  the  business.  This  information  is  generally 
passed  on  from  man  to  man  by  word  of  mouth.  Usually  there  is  no 
written  statement  giving  in  condensed  form  a  bird's-eye  view  of  the 
whole  history  and  present  field  of  the  corporation.  Broadly,  it  is  now 
almost  impossible  for  any  new  director  in  a  corporation  to  give  an 
intelligent  director's  vote  on  any  proposition  brought  up  within  a  year 
after  he  has  joined  the  directorate. 

It  will  not  be  long  before  every  man  holding  the  position  of  a  corpora- 
tion director  or  a  corporation  executive  will  be  able  to  read,  quickly 
and  intelligently,  simple  curves  and  figures  like  those  combined  on  the 
curve  cards  here.  With  a  card-index  file  of  curves  and  a  record  depart- 
ment like  that  described  in  this  chapter,  it  should  be  possible  for  any 
trained  man  coming  into  a  corporation  as  a  new  director  or  new  official 
to  give  a  fairly  intelligent  vote  after  only  half  a  day's  study  of  the 
curves,  and  this  too  without  having  spoken  a  single  word  to  anyone. 
If  the  record  department  and  the  curves  are  properly  kept,  the  whole 
situation  would  be  shown  on  the  face  of  the  cards  with  far  more  clearness 
than  it  would  ordinarily  be  possible  to  give  by  words  alone,  even  if 
the  whole  history  and  present  status  of  the  corporation  were  told. 

Consider  the  value  of  a  record  department  like  that  suggested,  if 
such  a  department  were  part  of  the  equipment  of  the  mayor's  office  of 
any  city.  The  department  could  be  maintained  continuously  by  civil- 
service  employees  who  could  keep  the  records  in  standardized  form  year 
after  year,  no  matter  what  shake-ups  there  might  be  in  political  parties 
and  in  spite  of  the  numerous  changes  in  personnel  usual  when  one  set  of 
city  officers  follow  another  with  great  rapidity.  In  municipal  work 
there  would  be  no  necessity  for  keeping  any  except  the  original  curve 
cards  under  lock  and  key,  as  all  the  information  would  be  public 
property  and,  of  course,  available  to  properly  authorized  persons.  It 
would  certainly  make  a  great  difference  to  any  new  mayor  if  he  could 


RECORDS  FOR  THE  EXECUTIVE  299 

go  to  a  record  room  and  study  a  set  of  curves  showing,  for  instance,  the 
total  number  of  men  in  the  employ  of  the  city  year  after  year  under 
different  administrations.  He  would  be  able  to  see  over  a  period  of 
years  the  number  of  men  in  each  city  department  such  as  fire,  police, 
street-cleaning,  etc.,  together  with  the  average  rate  of  pay.  He  would 
also  have  complete  information  over  a  long  series  of  years  regarding 
taxable  property  in  the  city,  tax  rates,  total  population,  death  rates, 
etc.  All  this  information  would  be  available  instantly,  not  only  to  the 
mayor  but  to  each  member  of  the  council,  who  might  apply  to  the  record 
department  very  much  as  he  would  apply  to  any  good  reference  library 
when  in  search  of  information.  The  only  rule  necessary  would  be 
that  no  curve. cards  should  leave  the  room.  To  safeguard  information 
files  to  which  numerous  councilmen  have  access,  it  would  be  wise  to  use 
only  blue  prints  in  the  open  files,  keeping  the  original  cards  in  separate 
locked  files,  available  only  to  the  man  who  plots  the  data  on  each  card, 
point  by  point,  as  information  is  received.  Councilmen,  civic  organiza- 
tions, newspapers,  etc.,  wanting  copies  of  any  record  card  should 
be  able  to  get  blue  prints  or  photographs  at  a  nominal  charge  of  say 
ten  cents  per  card  copy.  The  New  York  Public  Library  is  successfully 
working  a  plan  by  which  photographs  of  any  page  of  any  book  in  the 
library  can  be  provided  to  readers  in  a  few  hours  at  a  cost  of  only 
twenty-five  cents  per  page.  A  similar  plan  could  be  used  for  the  sug- 
gested copies  of  official  curve  records. 

Progress  in  the  government  of  the  world,  and  especially  in  the 
government  of  cities  and  of  industrial  corporations,  has  been  greatly 
retarded  by  the  fact  that  the  only  information  available  to  executive 
officers  has  been  provided  to  the  executive  in  the  form  which  is  most 
convenient  for  the  use  of  the  accountant.  It  is,  of  course,  necessary 
that  records  should  be  kept  accurately  from  the  standpoint  of  good 
accounting,  and  the  author  has  no  complaint  to  make  of  accounting 
methods  in  so  far  as  accuracy  is  concerned.  It  is  not,  however,  right 
that  executive  officers  who  must  determine  policies  and  who  must  make 
instant  decisions  should  be  forced  to  base  all  their  decisions  on 
information  provided  to  them  only  in  the  form  of  the  accountant's 
standard  arrangement  of  balance  sheet  and  operating  statement. 

The  accountant  must  necessarily  take  a  bird's-eye  view  of  the 
whole  business  from  time  to  time,  so  that  he  may  see  how  all  the  com- 
ponent parts  add  together,  to  make  certain  that  he  gets  a  balance. 
The  result  is  that  the  accounting  officer  usually  makes  up  a  periodic 


300  GRAPHIC   METHODS 

report,  in  which  he  gives  at  the  end  of  any  month  or  at  the  end  of  any 
year  a  complete  bird's-eye  statement  of  the  status  of  the  business 
at  that  particular  time.  Because  of  the  nature  of  his  problems,  the 
executive's  mind  must  necessarily  work  in  a  manner  absolutely  dif- 
ferent from  that  of  the  mind  of  the  accountant.  The  executive  does 
not  often  want  a  bird's-eye  view  of  his  whole  business  at  any  one 
period  of  time.  What  the  executive  must  have  is  a  cross-index  of  the 
accountant's  information,  so  that  he  may  see  over  a  long  period  of 
time  the  whole  history  of  any  portion  of  his  business.  Most  managers 
are  forced  to  work  from  the  accountants'  monthly  statement,  and 
their  procedure  is  accordingly  to  go  through  the  separate  operating 
statements  for  several  months  and  take  off  on  scratch  pads  the  figures 
for  the  items  in  which  they  may  be  particularly  interested  at  the 
moment.  These  figures  may  have  to  be  added  together  in  order  to 
compare  a  certain  number  of  months  this  year  with  the  same  months 
of  last  year.  This  work  not  only  takes  the  time  of  the  highest  paid 
man  in  the  organization,  but  the  hasty  scratch-pad  figures  are  likely 
to  contain  errors.  It  is  absurd  that  executive  officers  should  be  forced 
to  make  their  own  cross-indexes  of  the  accountant's  statement,  and 
not  only  make  these  cross-indexes  but  make  them  while  holding  the 
long-distance  telephone  or  at  other  rush  times  when  seconds  are 
important. 

The  information  as  it  comes  from  the  accountant's  office  should  be 
passed  to  the  man  in  the  executive  department  whose  function  it  is 
to  provide  information  for  the  executive  by  cross-indexing  all  in- 
formation from  the  accountant's  reports  and  putting  this  information 
in  the  form  of  curves.  The  accountant's  report  would,  of  course,  be 
filed  carefully  for  future  reference  purposes  if  reference  is  ever  neces- 
sary, but  for  the  purposes  of  the  executive  the  curve  cards  with  the 
figures  they  contain  are  sufficient.  Not  only  is  the  information  for 
any  subject  shown  on  the  cards  as  a  curve  over  a  long  period  of  time, 
but  the  actual  figures  of  the  accountant's  report  are  visible  in  such 
manner  that  they  may  be  found  instantly  and  quoted  directly  from  the 
curve  cards  without  having  to  refer  back  month  by  month  to  the 
original  figures  in  the  accountant's  report. 

The  manager  or  chief  executive  of  any  business  using  curves  in 
order  to  keep  in  close  touch  with  all  departments  will  find  that  he 
needs  a  liberal  education  in  logic  to  enable  him"  to  draw  the  correct 
conclusions  quickly  from  the  large  number  of  facts  available.     There 


RECORDS  FOR  THE  EXECUTIVE  301 

are  certain  general  principles  which  are  gradually  being  recognized, 
and  which  within  the  next  few  years  will  doubtless  be  well  enough  known 
to  classify  and  make  available  for  the  executive's  use.  At  present, 
however,  each  executive  must  work  out  for  himself  his  own  means 
of  recording  data  and  of  determining  policies  in  operating  his  business. 
An  example  showing  some  of  the  difficulties  involved  in  correct  inter- 
pretation is  one  concerning  overhead-expense  ratios.  Some  managers 
consider  the  ratio  of  indirect  expenses  to  the  direct  labor  in  any  de- 
partment of  a  manufacturing  business  as  an  infallible  barometer  by 
which  each  department  of  the  business  can  be  run.  They  little  realize 
the  absurdity  of  paying  too  much  attention  to  overhead-expense 
ratios  and  the  danger  to  the  business  of  using  overhead-expense  ratios 
as  a  yard-stick  by  which  to  measure  accomplishment.  In  this  par- 
ticular case,  that  of  a  large  manufacturing  plant,  a  new  department 
manager  changed  the  manufacturing  methods  so  radically  that  he 
was  able  to  produce  an  increased  output  with  less  than  half  the  former 
payroll  for  direct  labor.  The  expenses  for  the  foremen,  clerks,  sup- 
plies, etc.,  in  the  department  remained  about  the  same  as  before. 
Because  of  the  reduced  amount  of  direct  labor  the  overhead-expense 
ratio  was  of  course  doubled,  much  to  the  astonishment  of  the  chief 
executive,  who  accordingly  considered  this  department  as  the  worst 
managed  in  his  whole  works.  This  executive  had  been  running  his 
plant  for  so  many  years  on  the  expense-ratio  basis  that  the  new  de- 
partment head  found  it  almost  impossible  to  convince  the  chief  ex- 
ecutive that  the  department  was  making  money  more  rapidly  than 
ever  before,  even  though  the  overhead-expense  ratio  had  doubled. 
The  overhead  expense  itself  had  not  increased,  and  the  ratio  was 
doubled  simply  because  the  amount  of  direct  labor  had  been  de- 
creased. 

It  is  perhaps  worth  while  to  point  out  here  that  there  is  danger 
in  giving  too  much  information  and  too  many  facts  to  executives 
of  small  brain  capacity  who  do  not  know  how  to  use  their  authority 
intelligently.  Curves  such  as  those  described  in  this  and  the  preceding 
chapter,  placed  for  the  first  time  in  the  hands  of  the  executive  who 
does  not  know  the  technology  or  the  general  underlying  principles 
of  the  business  which  he  controls,  are  likely  to  prompt  such  a  narrow- 
minded  director  to  send  out  a  regular  deluge  of  letters  unjustly  crit- 
icising the  actions  of  his  subordinates.  There  is  a  possibility  that  a 
small-caliber  man  in  the  manager's  chair  may  send  out  too  much 


302  GRAPHIC    METHODS 

destructive  criticism  and  not  enough  constructive  criticism.  If  such 
a  misfortune  should  occur  it  would  cause  every  department  head  in 
the  organization  to  withhold  information  and  consider  the  whole 
curve-record  system  as  a  new  form  of  diabolical  torture.  Curves  are 
not  intended  to  give  any  chief  executive  an  excuse  to  "jump  on"  any  de- 
partment manager  or  foreman.  The  curve  records  are  intended  only 
to  point  out  those  danger  points  at  which  construction  work  is  needed. 
An  executive  of  the  right  type  will  soon  realize  as  he  uses  the  curves 
that  he  must  do  the  constructive  work  himself,  and  that  the  curves 
will  really  have  more  effect  in  changing  the  procedure  in  his  own 
office  than  in  changing  the  detailed  routine  in  the  departments  of 
his  various  subordinates. 

One  of  the  first  tasks  confronting  any  modern  executive  is  that 
of  training,  on  the  one  hand,  his  board  of  directors  and  executive 
committee,  and  on  the  other  hand,  his  various  department  heads  and 
their  subordinates,  to  read  curves  accurately  so  that  the  facts  pre- 
sented may  be  intelligently  grasped  and  applied  to  the  benefit  of  the 
business  as  a  whole.  It  is  unfortunate  that  so  many  men  serving 
to-day  on  boards  of  directors  and  in  executive  positions  of  large  busi- 
nesses are  not  able  to  read  even  the  simplest  curve  with  any  real 
grasp  of  the  facts  portrayed.  Engineers  and  other  trained  men  who 
have  real  facts  available  are  tremendously  handicapped  in  presenting 
the  facts  if  it  is  not  feasible  to  use  the  graphic  method  of  presentation. 
A  man  prepared  to  show  his  data  in  the  form  of  curves,  for  example 
like  Fig.  157  or  Fig.  159,  feels  that  he  would  have  an  almost  hopeless 
task  to  convey  the  vital  facts  if  only  spoken  words  might  be  used. 
The  writer  ventures  to  predict  that  within  ten  years  practically  all 
corporation  directors  and  executives  will  be  able  to  interpret  curves 
with  satisfaction  to  themselves  and  with  great  benefit  to  their  business. 
The  executive  who  cannot  read  curves  will  in  the  near  future  be  the 
exception  rather  than  the  rule. 

If  any  general  manager  will  take  the  trouble  to  train  his  department 
heads  to  read  curves  and  will  then  supply  to  them  curves  showing  the 
facts  of  his  business,  he  will  be  tremendously  repaid  in  the  interest, 
enthusiasm,  and  real  progress  toward  improvement  which  will  be 
aroused  in  his  men. 

It  is  possible  to  use  a  reflecting  lantern  like  that  pictured  in  Fig. 
218  to  show  on  a  screen  the  curves  from  the  curve  cards  described  in 
Chapter  XIII.     Lantern  slides  are  not  practicable  when  frequent  meet- 


RECORDS  FOR  THE  EXECUTIVE 


303 


ings  of  department  heads  must  be  held.  The  expense  of  making 
lantern  slides  each  time  a  new  point  is  plotted  on  each  curve  would  be 
too  great  for  even  the  largest  corporations.  Another  disadvantage  of 
using  lantern  slides  is  the  impossibility  of  getting  slides  made  quickly 
enough  to  represent  always  the  latest  points  plotted  on  the  curves.  By 
using  the  original  curve  cards  directly  in  the  reflecting  lantern  there  is 
always  a  certainty  that  the  picture  shown  on  the  screen  represents  the 
very  latest  data  which  are  available  in  curve  form.  When  these  curve 
cards  are  used  in  a  reflecting  lantern  a  simple  slide  carriage  is  made 


Fig.  218.    Reflectoscope  as  Made  by  A.  T.  Thompson  &  Co.,  Boston,  Mass. 

Lantern  slides  may  be  used  as  shown  at  the  top  of  the  picture.  The  stand  holding  the  book  may  be  replaced 
by  a  simple  carriage  arranged  to  take  the  4-by-6-inch  and  the  4-by-12-inch  curve  cards.  The  very 
latest  data  from  the  file  shown  in  Fig.  217  may  then  be  instantly  reflected  onto  a  screen  for  use  in  a 
meeting  of  the  department  heads  of  a  business. 

to  replace  the  stand  holding  the  book  in  Fig.  218.  As  the  card  is  laid 
down  flat  in  its  natural  position  and  in  plain  view  of  the  operator,  there 
is  no  likelihood  of  cards  being  put  into  the  machine  incorrectly.  If  a 
carriage  about  two  feet  long  is  used,  the  carriage  may  be  moved 
alternately  from  right  to  left,  and  while  one  side  contains  the  cards 
which  are  being  reflected  on  the  screen,  the  other  side  may  be  loaded 
with  the  cards  next  desired.  On  account  of  its  length  the  carriage 
will  hold  curve  cards  for  several  succeeding  years.  By  pushing  the 
carriage  slowly  across  the  lantern  the  fluctuation  in  any  curve  may 
be  shown  for  as  long  a  series  of  years  as  may  be  desired.  Simple  spring 
clips  on  the  carriage  may  be  used  to  hold  the  overlapping  cards  in  their 


304  GRAPHIC    METHODS 

exact  position.  Not  only  are  the  curves  themselves  shown  on  the  screen, 
but  the  whole  face  of  the  card  is  seen  so  that  the  figures  for  any  points 
on  the  curve  which  are  of  special  interest  may  be  read  directly  from 
the  screen. 

If  the  information  or  record  room  is  large  enough  to  serve  for  holding 
conferences  the  lantern  and  the  screen  may  be  installed  permanently 
as  part  of  its  equipment.  Ordinarily,  however,  it  will  be  found  best 
to  have  the  record  room  more  private  than  any  room  used  for  general 
conferences  can  be  made,  and  the  lantern  would  be  part  of  the  equip- 
ment of  the  conference  room  rather  than  of  the  record  room.  With  this 
arrangement  it  will  be  necessary  to  take  the  curve  cards  from  the  record 
room  to  the  place  where  the  lantern  is  installed.  The  file  for  the  curve 
cards  (see  Fig.  217)  had  better  be  equipped  with  spring  locks  so  that 
there  will  be  no  danger,  when  the  file  is  carried,  of  drawers  slipping  out 
and  spilling  the  cards.  A  rod  arrangement  is  never  desirable  with  such 
cards  as  these,  for  the  rod  would  spoil  the  bottom  portion  of  the  card 
and  would  also  make  it  impossible  to  lift  cards  out  for  quick  reference 
or  comparison.  Brass  handles  on  the  sides  of  the  file  case  would  make 
it  easy  to  carry  the  case  to  the  conference  room.  There,  on  a  table 
beside  the  lantern,  the  cards  in  the  file  case  would  be  available  for  use 
almost  exactly  as  lantern  slides  are  used  with  the  ordinary  lantern.  In 
fact,  the  arrangement  of  the  cards  is  even  more  convenient  than  the 
usual  arrangement  of  lantern  slides  in  that  the  cards  have  a  guide  index 
so  that  any  desired  card  may  be  instantly  located. 

An  executive  who  wishes  to  have  a  meeting  of  his  department  heads 
need  not  make  any  very  definite  plan  before  the  meeting  begins  as  to 
what  cards  he  is  to  show  on  the  screen.  He  can  start  talking  to  his 
men,  and,  at  pleasure,  ask  the  lantern  operator  (ordinarily  the  statis- 
tician) for  any  set  of  curve  cards  which  may  be  of  interest  to  him  at 
the  moment,  or  which  may  be  referred  to  at  any  time  during  the  dis- 
cussion. The  use  of  curves  on  a  lantern  screen  in  the  manner  suggested 
would  entirely  revolutionize  the  meetings  of  the  department  heads  of 
a  business,  or  the  meetings  of  branch-house  sales  managers.  In  sales 
work  especially,  the  use  of  the  various  cards  would  make  it  possible  to 
show  the  whole  assembly  the  recent  records  made  by  selling  houses  in 
the  different  parts  of  the  country.  The  cards  for  those  houses  which 
made  particularly  good  records  could  be  shown,  the  records  could  be 
commended,  and  conclusions  could  be  drawn  as  to  how  the  success 
had  been  attained.     Records  for  the  less  successful  houses  could  also 


RECORDS  FOR  THE  EXECUTIVE 


805 


Fig.  219.  Curves  on  Swinging-leaf  Display  Fixtures  Used  for  Ready  Reference  in 
the  Office  of  Day  and  Zimmermann,  Philadelphia.  Each  Leaf  May  Be  Easily 
Carried  to  a  Desk  when  Additional  Points  Are  to  Be  Plotted  on  the  Curves 

This  same  type  of  display  fixture  is  often  convenient  for  showing  pin  maps  of  different  territories 

be  shown,  with  comments  by  the  sales  manager  giving  his  own  sugges- 
tions and  asking  for  suggestions  from  the  other  branch-house  managers 
present. 

Reflecting  lanterns  can  be  used  at  directors'  meetings  as  soon  as 
corporation  directors  know  how  to  read  curves.  By  using  the  lantern, 
the  president  could  show  facts  relating  to  the  business  much  more 
rapidly,  much  more  clearly,  and  with  greater  accuracy  than  would  be 
possible  with  any  spoken  words.  The  showing  of  curves  would  give 
the  directors  a  chance  to  check  the  president's  statements  so  that  there 
would  be  less  danger  than  at  present  of  a  corporation  president  so 
choosing  his  words  that,  though  the  words  might  be  strictly  truthful  in 
themselves,  they  would  be  over-optimistic  because  they  did  not  tell 
all  the  truth.  The  presence  of  the  whole  file  of  curve  cards  immediately 
beside  the  lantern  would  enable  any  director  to  call  for  facts  relating 
to  any  phase  of  the  business  on  which  he  might  desire  information.  The 
use  of  these  curve  cards,  and  a  lantern,  would  permit  a  properly  educa- 
ted set  of  directors  really  to  direct  the  business  for  which  they  are 
responsible  to  the  stockholders. 


306  GRAPHIC   METHODS 

It  is  sometimes  desirable  to  have  the  chief  facts  relating  to  a  business 
plotted  on  wall  charts  which  are  instantly  visible  in  a  conference  room. 
Fig.  219  was  photographed  in  the  record  room  which  adjoins  the  direc- 
tors' room  of  Day  and  Zimmermann,  of  Philadelphia.  On  the  swing- 
ing-leaf fixtures  a  series  of  curves  are  plotted  giving  all  the  salient 
facts  relating  to  a  group  of  public-service  corporations.  Though  this 
type  of  wall  chart  is  in  many  cases  desirable,  there  are  limitations  to 
the  use  of  wall  charts  because  the  number  of  charts  cannot  be  suffi- 
ciently increased  to  give  all  the  detailed  information  which  is  usually 
necessary.  Wall  charts  are  suitable  chiefly  to  furnish  summarized 
information  to  directors  or  other  men  whose  time  is  limited  or  who  come 
to  an  office  only  at  rare  intervals. 

Wall  exhibits  of  curves  can  sometimes  be  used  with  satisfactory 
results  if  special  care  is  taken  to  draw  the  curves  on  a  very  large  scale 
and  arrange  them  on  all  four  walls  of  a  room.  A  prominent  financier 
of  New  York  City  is  said  to  have  a  large  room,  on  the  top  floor  of  his 
residence,  where  the  walls  are  completely  covered  with  curve  charts 
on  which  points  are  plotted  as  rapidly  as  data  can  be  obtained.  This 
man  is  so  limited  for  time  that  he  keeps  in  touch  witli  general  financial 
conditions  by  referring  to  the  charts  in  this  room  for  only  a  brief 
time  each  evening.  He  disappears  to  his  reference  room  to  meet 
his  private  secretary  immediately  after  dinner.  In  the  center  of  the 
room  is  a  revolving  desk  chair  with  an  ash  tray  fastened  to  one  arm. 
For  the  length  of  one  cigar  the  financier  sits  in  his  chair  slowly  re- 
volving the  chair  until  he  has  covered  the  information  given  on  all 
of  the  wall  charts,  perhaps,  if  necessary,  asking  a  few  brief  questions 
of  his  secretary.  Though  very  little  of  the  financier's  time  is  taken, 
he  is  able  by  concentrated  thought  on  the  facts  shown  by  his  wall 
charts  to  keep  in  full  touch  with  world  finance  and  to  map  out  his 
own  plans  for  future  operation. 


Chapter  XV 
CORPORATION  FINANCIAL  REPORTS 

THE  annual  report  of  a  corporation  is  usually  mailed  to  each 
stockholder.  The  report,  as  commonly  gotten  up,  contains  prac- 
tically nothing  except  a  brief  statement  by  the  president  in 
regard  to  the  last  year's  business,  together  with  the  balance  sheet 
and  operating  statement  furnished  by  the  accounting  officers  of  the 
company,  and  perhaps  an  audit  by  some  firm  of  certified  public  ac- 
countants. The  report  sent  to  a  stockholder  is  essentially  in  that 
form  necessary  for  the  auditor  to  check  the  financial  figures  and  to 
certify  to  their  being  in  balance  and  correct. 

Though  the  balance  sheet  and  operating  statement,  with  the  letter 
of  approval  by  the  certified  public  accountant,  are  necessary  and  de- 
sirable, they  do  not  contain,  in  themselves,  the  information  most 
desirable  and  most  intelligible  to  the  average  stockholder.  What  the 
stockholder  needs  most  is  a  report  from  which  he  can  make  comparison 
with  preceding  years.  The  bankers  and  large  investors  who  can  pre- 
serve in  their  files  annual  reports  of  a  corporation  over  a  long  period 
of  years  probably  number  less  than  one  per  cent  of  the  total  number 
of  stockholders  to  whom  the  annual  reports  are  sent.  It  is  only  in 
very  large,  well  managed  offices  that  a  file  of  corporation  reports  is 
made  so  that  a  complete  set  of  reports  for  a  long  period  of  years  is 
available  for  comparison  with  any  new  report  which  may  be  received. 
The  average  stockholder  cannot  preserve  his  annual  reports  from  year 
to  year  in  such  manner  that  he  can  lay  his  hands  on  the  earlier  reports, 
and  thus  compare  the  last  report  with  the  record  of  preceding  years. 
Even  if  every  stockholder  should  have  some  yet  uninvented  type  of 
filing  system  by  which  everything  is  preserved  and  everything  can  be 
found  instantly  when  needed,  that  would  not  solve  the  problem.  Stock- 
holders are  changing  so  rapidly  that,  of  the  total  number  of  stockholders 
to  whom  reports  are  sent  in  any  one  year,  a  comparatively  small  percent- 

307 


308  GRAPHIC   METHODS 

age  have  been  stockholders  for  more  than  two  or  three  years.  Because 
they  have  not  been  stockholders  for  any  length  of  time,  they  cannot  have 
available  the  annual  reports  of  earlier  years  to  compare  with  any  annual 
report  just  received.  The  only  way  a  new  stockholder  can  possibly 
determine  whether  he  wishes  to  buy  some  more  stock  or  sell  what 
stock  he  already  has,  is  to  hunt  up  some  other  stockholder  or  some 
banker  who  may  happen  to  have  a  file  of  the  annual  reports  over  a 
period  of  years.  Assuming  that  a  complete  file  of  annual  reports  can 
be  found,  most  stockholders,  if  left  to  their  own  resources,  would  be 
hopelessly  confused  in  trying  to  reach  any  correct  basis  for  analyzing 
the  figures.  Each  stockholder  would  have  to  take  a  sheet  of  paper 
and  copy  off,  into  different  columns  for  various  important  items  of 
the  operating  statement  and  balance  sheet,  figures  for  a  number  of 
years  so  that  the  figures  for  different  years  could  all  be  seen  at  one 
time  and  compared.  This  means  that  each  stockholder  would  have  to 
make  practically  a  cross-index  of  the  most  important  data  contained 
in  a  series  of  annual  reports  in  order  to  study  the  different  phases 
of  operation  independently.  Even  if  the  stockholder  should  know 
how  to  make  such  a  cross-index  properly,  there  are  very  few  stock- 
holders who  would  be  willing  to  give  the  time  and  the  mental  effort 
requisite  to  make  a  tabulated  comparison  of  the  kind  necessary. 

The  absorption  of  good  securities  by  the  public  has  increased  in 
the  last  ten  years  at  a  tremendous  rate.  The  Wall  Street  Journal 
has  compiled  statistics  of  the  stockholders  of  the  larger  railway  and 
industrial  corporations  showing  that  the  numbers  have  grown  as 
follows : 

1901 227,000 

1906 431,000 

1911 865,000 

1913 1,250,000 

Mr.  Samuel  Rea,  the  president  of  the  Pennsylvania  Railroad, 
recently  stated  that  there  are  nearly  100,000  stockholders  in  the 
Pennsylvania  Railroad  and  its  affiliated  companies,  and  that  the 
number  of  its  bondholders  probably  exceeded  200,000.  Therefore, 
if  there  are  1,250,000  stockholders  of  the  railways  and  industrial 
corporations,  there  are  doubtless  considerably  more  than  2,000,000 
bondholders.  Though  there  are  many  duplications  in  these  figures, 
the  fact  remains  that  the  prosperity  of  probably  3,000,000  investors 
is  largely  dependent  upon  the  success  of  these  corporations. 


i 


CORPORATION    FINANCIAL   REPORTS  309 

While  the  number  of  stockholders  has  been  increasing,  the  average 
holdings  of  each  stockholder  have  been  steadily  decreasing,  and  now 
average  ninety -eight  shares.  The  stocks  of  the  United  States  Steel 
Corporation  are  great  favorites  among  small  investors.  Taking  the 
stockholders'  list,  it  was  found  that  among  one  hundred  people,  chosen 
at  random,  only  nine  own  one  hundred  shares,  or  over,  of  both  preferred 
and  common  stock,  while  forty-seven  have  less  than  ten  shares  each. 

It  is  highly  desirable  that  corporations  shoidd  not  only  keep  their 
old  stockholders,  but  should  attract  new  ones.  The  surest  way  to 
accomplish  this  end  is  to  treat  stockholders  with  the  utmost  frankness. 
Although  considerable  publicity  is  already  given  to  the  affairs  of  the 
larger  corporations,  further  publicity  is  desirable.  The  average  stock- 
holder does  not  as  a  rule  understand  a  balance  sheet,  and  has  only  the 
vaguest  idea  of  his  company's  affairs.  So  long  as  dividend  payments 
are  maintained,  he  is  content.  To  be  sure,  a  stockholder  can  always 
get  an  impartial  and  valuable  opinion  from  an  investment  banker  con- 
cerning the  past  records  and  future  prospects  of  any  company,  but  it 
would  be  well  if  the  annual  reports  of  boards  of  directors  to  stock- 
holders contained  material  from  which  the  investor  could  judge  for 
himself  to  a  greater  extent.  The  material  included  should  show  the 
records  of  the  company  over  a  period  of  years,  for  the  company's 
achievement  in  any  one  year  may  be  unnecessarily  discouraging,  or 
fictitiously  encouraging.  These  records  are  most  easily  understood 
when  put  in  graphic  form.  With  such  graphic  presentations  any 
stockholder  can  learn  instantly  how  the  fiscal  year  under  review 
compares  with  the  several  years  preceding. 

The  American  Telephone  and  Telegraph  Company  have  for  several 
years  shown  on  the  back  cover  of  their  annual  report  a  chart  like  Fig. 
249  portraying  the  growth  in  their  business.  Fig.  2  also  appeared 
in  an  annual  report  of  the  same  corporation  to  give  a  clear  conception 
of  what  becomes  of  the  company's  revenue. 

Though  Fig.  1  has  not  been  used  in  any  annual  report,  it  shows  a 
type  of  chart  which  could  very  readily  be  included  in  a  financial  report 
to  give  complete  facts  to  stockholders  regarding  complex  conditions 
on  which  the  average  stockholder  would  gather  very  little  information 
from  the  kind  of  corporation  financial  report  ordinarily  sent  to  him. 

The  railroads  have  used  charts  in  their  annual  reports  to  a  greater 
extent  than  the  industrial  corporations.  Some  of  the  railroad  charts, 
however,  are  not  put  up  in  such  form  as  to  be  easily  understood  and, 


310 


GRAPHIC    METHODS 


with  many  of  the  charts,  there  is  danger  of  misinterpretation.  For 
instance,  it  is  not  at  all  easy  to  analyze  Fig.  220  so  that  its  four  dif- 
ferent subjects  may  be  compared. 


PER  CENT  OF  INCREASE  OVER  1902                                                         | 

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Fig.  220.  Percentage  Increase  in  Freight  Service  on  the 
Illinois  Central  Railroad  Since  1902.  This  Illustra- 
tion Was  Taken  from  the  19 12  Annual  Report  of  the 
Company 

Four  distinct  subjects  are  treated  in  this  chart,  but  the  horizontal  bars 
are  arranged  in  such  manner  that  the  reader  is  likely  to  think  there 
is  only  one  subject.  Probably  most  readers  would  prefer  to  turn 
the  chart  so  that  it  may  be  read  from  the  left-hand  edge  as  four 
separate  curves.  To  a  trained  reader  this  information  would  be  much 
more  clear  if  put  in  the  form  of  curves  like  those  seen  in  Figs.  224, 
225,  226,  227 

Fig.  221  also  shows  several  different  subjects  which  should  be 
compared,  but  for  which  comparison  is  not  very  feasible  on  the  chart 
as  given.  In  Fig.  220  the  four  different  subjects  were  so  widely  sep- 
arated that  comparisons  were  almost  impossible,  while  in  Fig.  221  the 
four  different  subjects  have  the  bars  so  arranged  that  it  is  difficult 
for  the  eye  to  follow  any  one  subject  through  the  maze  of  bars. 

In  Fig.  222  the  method  of  presentation  is  somewhat  similar  to 
that  used  in  Fig.  221.     As  seen  in  Fig.  222,  however,  the  bars  are 


CORPORATION    FINANCIAL    REPORTS 


311 


arranged  horizontally  with  the  earlier  year  at  the  bottom,  while  in 
Fig.  221  the  bars  are  arranged  vertically  with  the  earlier  year  at  the 
right.  In  both  of  these  charts  the  arrangement  for  successive  years 
is  incorrect,  for  the  charts  give  the  impression  that  all  quantities  por- 
trayed are  becoming  less  in- 
stead of  greater  as  years  go  on. 
The  indiscriminate  mixture  of 
so  many  different  kinds  of 
bars  in  one  chart  makes  a 
complex  diagram  to  interpret, 
and  it  is  probable  that  the 
chart  would  at  least  be  no 
more  difficult  to  apprehend  if 
made  entirely  in  the  form  of 
curves  instead  of  bars. 
Though  it  is  true  that  curves 
are  not  understood  by  some 
people  who  can  readily  grasp 
the  bar  method  of  presenta- 
tion, there  is  no  use  in  keeping 
to  the  bar  method  if  the  bar 
presentation  is  made  as  com- 
plex as  a  chart  involving 
curves. 

Fig.  223  was  not  printed  in 
a  corporation  annual  report, 
but  it  is  included  here  because 
it  may  show  some  possibility 
for  the  inclusion  of  curves 
in  financial  reports  to  give  the 
stockholder  more  complete 
information  than  he  would 
otherwise  receive.  The  data 
of  Fig.  223  are  of  interest 
when   considered   along   with 


Fig.  221.  Freight  Service  and  Traffic  on  the 
Union  Pacific  Railroad  and  Auxiliary  Com- 
panies 

This  chart  shows  by  years  the  per  cent  of  increase  over  the 
year  ended  June  30,  1898,  in  the  gross  revenue  from  the 
transportation  of  commercial  freight,  the  number  of 
tons  of  commercial  freight  carried  one  mile,  and  the 
number  of  miles  run  by  cars  and  locomotives  in  freight- 
train  service.  Locomotive  miles  include  revenue 
freight-train  miles,  all  mixed-train  miles,  and  helping- 
train  miles 

The  illustration  is  reduced  from  the  1912  annual  report 
to  stockholders.  The  backward  arrangement  of 
years  from  right  to  left  causes  the  first  impression  that 
all  quantities  are  growing  less  instead  of  greater. 
Four  subjects  shown  combined  in  one  chart  in  this 
manner  are  confusing.  Either  four  distinct  groups  of 
bars  or  four  curves  would  be  superior  to  the  method 
used  here 


the  charts  seen  in  Fig.-  224,  Fig.  225,  Fig.  226,  and  Fig.  227.  Fig. 
223  is,  however,  misleading  because  the  vertical  scale  does  not  extend 
to  zero  and  the  chart  gives  the  impression  of  a  much  larger  per- 
centage difference  between  net   earnings   and   dividends   than   really 


312 


GRAPHIC    METHODS 


existed.  Omitting  the  bottom  of  the  chart  makes  the  dividends 
appear  a  smaller  percentage  of  net  earnings  than  they  really  were. 
Fig.  223  could  have  been  considerably  improved,  also,  if  the  line 
showing  net  earnings  were  made  much  heavier  than  it  is  seen  in  the 
illustration. 


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Union  Pacific  Railroad 

Fig.  222.    Passenger  Service  and  Traffic  on  the  Union 
Pacific  Railroad  and  Auxiliary  Companies 

This  chart  shows  by  years  the  per  cent  of  increase  over  the  year  ended 
June  30,  1898,  in  the  gross  revenue  from  the  transportation  of  passen- 
gers, the  number  of  passengers  carried  one  mile,  and  the  number  of 
miles  run  by  cars  and  locomotives  in  passenger-train  service.  Loco- 
motive miles  include  revenue  passenger-train  miles,  all  mixed-train 
miles  and  helping  passenger-train  miles,  but  do  not  include  miles  run 
by  motor  cars 

Here  the  reversed  arrangement  with  the  latest  year  at  the  top  gives  the 
erroneous  impression  that  passenger  business  is  decreasing.  A  chart 
like  this  does  not  assist  greatly  in  conveying  information  to  the  stock- 
holder 

What  figures  for  an  annual  report  should  always  be  shown  in 
chart  form  to  make  comparisons  most  clear  is  hard  to  determine, 
but  it  will  doubtless  be  agreed  that,  if  possible,  the  charts  should 


CORPORATION    FINANCIAL   REPORTS 


313 


001  Jd: 

1902          1903          1904          190.5          1906          1907          1908          1909          1910          1911          1912 

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New  York  Titucs  Annalist 

Fig.  223.    Net  Earnings  and  Dividends  of  the  United  States  Steel  Corporation 

The  figures  for  net  earnings  are  plotted  by  quarters.  Dividend  figures  are  plotted  to  show  the  total  divi- 
dends each  year.  The  line  at  the  top  of  the  shaded  area  shows  the  dividend  paid.  Dividends  exceed 
net  earnings  in  portions  of  the  years  1911  and  1912,  but  the  total  earnings  of  those  years  were  nevertheless 
great  enough  to  justify  maintaining  the  dividend  rate 

Though  this  illustration  contains  some  interesting  information,  the  chart  is  misleading  because  the  scale 
does  not  extend  to  zero.  At  first  glance,  the  dividend  of  1909  would  seem  to  be  more  than  four  times 
the  dividend  of  1908  when  in  reality  it  is  only  about  twice  as  large 

attempt  an  answer  to  these  questions  that  naturally  arise  in  the  stock- 
holder's mind: 

1.  Has  the  earning  power  of  the  company  been  maintained? 

2.  Is  the  property  being  kept  in  proper  physical  condition? 

3.  Is  the  financial  condition  sound? 

For  the  purpose  of  illustrating  the  advantages  of  the  graphic 
method  for  annual  reports,  the  United  States  Steel  Corporation  has 
been  selected.  The  chart  shown  in  Fig.  224  is  designed  to  answer  the 
first  question:  "Has  the  earning  power  of  the  company  been  main- 
tained?" In  order  to  bring  out  more  clearly  the  very  important 
relation  between  the  surplus  for  dividends  and  the  dividends  paid, 
curves  Nos.  3  and  4  are  redrawn  on  a  considerably  enlarged  scale 
as  seen  in  Fig.  225.  Curves  No.  3  and  No.  5  are  therefore  identical, 
as  are  also  curves  No.  4  and  No.  6. 

Fig.  224  and  Fig.  225  show  that  the  Steel  Corporation,  like  a 
large  number  of  railways  and  industrial  companies,  reached  the  zenith 


314 


GRAPHIC    METHODS 


DOLLARS 
I.  OOO,  OOO,  OOO 
900, OOO, OOO 
800,  OOO,  OOO 
700,  OOO,  OOO 
600,  OOO,  OOO 
500,  OOO,  OOO 
400,  OOO,  OOO 
300,  OOO,  OOO 
200,  OOO,  OOO 
lOO,  OOO.  OOO 


02  '03  '04  '05  '06  '07  '08  '09  '10  'II   '12 

Fig.  224.    The  Earning  Power  of  the  United  States  Steel  Corporation 

Curve  1.     Gross  earnings 

Curve  2.     Operating  expenses 

Curve  3.     Surplus  earned  available  for  dividends 

Curve  4.     Preferred  and  common  dividends  paid 

This  chart  and  the  following  charts  relating  to  the  United  States  Steel  Corporation  arc  submitted  as  a  sug- 
gestion to  show  how  the  annual  report  of  a  corporation  could  easily  give  comparisons  over  several  years. 
The  space  required  for  the  charts  is  insignificant,  yet  the  stockholders  would  receive  the  vital  facts  in 
such  form  as  to  permit  a  full  understanding  of  the  condition  of  their  company  as  compared  with  previous 
years 

of  its  earning  power  in  the  year  1907.  In  that  year  more  than  15 
per  cent  was  earned  on  the  common  stock,  while  only  2  per  cent  was 
paid.  Curve  No.  1  shows  that  the  gross  earnings  in  1907  were  $757,- 
000,000.  Then  follows,  in  1908,  the  terrific  slump  in  business  due  to 
the  financial  panic,  with  a  gradual  but  uncertain  recovery.  By  1912, 
the  corporation  succeeded  in  bringing  its  gross  business  up  to  $745,- 
000,000,  still  somewhat  under  the  1907  high-water  mark. 

The  movement  of  operating  expenses  is  depicted  by  curve  No.  2. 
A  glance  at  the  chart  shows  that,  during  1905-6-7,  gross  earnings 
tended  to  increase  faster  than  operating  expenses,  which  is  again  true 
in  1909  and  1910.  In  1908  and  1911,  it  proved  impossible  to  reduce 
operating  expenses  to  conform  to  the  reduction  in  gross  earnings, 
with  the  result  that  profits  were  sharply  reduced  in  both  these  years. 
In  1912,  a  unique  situation  occurs.  Curves  1  and  2  run  practically 
parallel,  showing  that  although  the  gross  earnings  were  largely  in- 
creased, operating  expenses  kept  pace.  The  largest  factor  in  op- 
erating expenses  is  naturally  labor,  and  the  reports  of  the  corporation 


CORPORATION    FINANCIAL    REPORTS 


315 


5 
6 


DOLLARS 

200,  OOO,  OOO 

180,  OOO,  OOO 

I60,  OOO,  OOO 

I40,  OOO,  OOO 

120,  OOO,  OOO 

lOO,  OOO,  OOO 

80,  OOO,  OOO 

60,  OOO,  OOO 

•40,  000,  000 

20,  000,  000 


'02  '03  '04  '05  '06  '07  '08  '09  '10  '11  '12 

Fig.  225.    The  Surplus  Earned  and  the  Dividends  Paid  by  the  United  States 

Steel  Corporation 

Curve  5.     Surplus  earned  available  for  dividends 
Curve  6.     Preferred  and  common  dividends  paid 

These  curves  are  the  same  as  Curve  3  and  Curve  4,  respectively.     The  data  are  depicted  here  on  a  large 
scale  so  that  the  relation  of  dividends  to  surplus  earned  may  be  seen  clearly 

throw  the  necessary  light  on  this  item.  The  average  wages  per  man 
in  1907  were  $765  per  annum,  and  in  1912,  $857.  It  has  been  shown 
that  gross  earnings  in  1912  were  less  by  $12,000,000  than  in  1907, 
yet  operating  expenses  in  1912  were  $45,000,000  more  than  in  1907, 
being,  as  the  curve  show^s,  over  $600,000,000  for  the  first  time  in  the 
Corporation's  history. 

Curves  3  and  5,  representing  the  surplus  for  dividends,  are  of  most 
interest  to  the  stockholder.  It  will  be  recalled  that  when  the  Steel 
Corporation  was  organized  in  1901,  the  common  stock  w^as  imme- 
diately placed  on  a  4  per  cent  basis.  In  1903  the  disbursements  to 
the  common  stock  ceased  altogether  and  even  the  7  per  cent  upon 
preferred  was  seriously  questioned.  During  1906,  1907,  and  1908, 
2  per  cent  was  paid  on  the  common,  and  then  in  1909,  the  rate  was 
first  raised  to  3  per  cent,  later  to  4  per  cent,  and  finally  to  5  per  cent. 
Conservative  people  have  always  criticised  the  5  per  cent  dividend, 
believing  that  a  4  per  cent  rate  would  be  more  likely  to  be  permanent. 
How^ever,  a  consideration  of  the  relation  of  curve  No.  5  with  No.  6 
will  show  that  the  Corporation  has  avoided  the  payment  of  unearned 
dividends  throughout  its  career.     The  margin  was  very  slim  in  1903 


316  GRAPHIC   METHODS 

and  1904  and  again  in  1911  and  1912.  As  the  balance  of  earnings 
for  the  common  stock  in  1911  was  only  5.9  per  cent  and  in  1912  only 
5.7  per  cent,  a  continuance  for  another  year  of  such  narrow  margin 
would  probably  have  meant  the  reduction  of  the  5  per  cent  rate, 
especially  in  view  of  the  reduced  appropriations  for  new  construction 
and  betterments,  as  disclosed  in  Fig.  226.  Fortunately,  however, 
for  the  stockholders,  conditions  in  1913  improved  enormously  and 
11.17  per  cent  was  earned  for  the  common  stock.  Considering  only 
the  figures  charted  here,  it  is  evident  that  the  earning  power  of  the 
Corporation  during  1912  was  not  maintained. 

To  answer  the  question  "Is  the  property  being  kept  in  proper 
physical  condition.^"  the  chart  shown  by  Fig.  226  has  been  constructed. 

As  seen  from  curve  7,  depreciation  and  repairs  have  shown  a  fairly 
constant  increase,  the  amount  in  both  1910  and  1912  exceeding  that 
of  1907,  although  the  gross  earnings  were  larger  in  1907  than  in  either 
1910  or  1912.     This  is  a  satisfactory  sign. 

Curve  8  portrays  the  total  amount  of  money  invested  in  the  con- 
struction of  new  plants,  mills,  etc.  This  curve  reaches  its  height 
in  1907  (running  up  to  $67,000,000)  and  represents  in  large  part  the 
creation  of  the  great  plant  at  Gary.  Curve  8  shows  that  even  the 
panic  of  1907  failed  to  curtail  new  construction  to  any  great  extent. 
But  the  poor  profits  in  1912,  coupled  with  the  higher  rate  of  dividend 
on  the  common  stock,  did  produce  a  sharp  contraction — from  $50,- 
000,000  in  1911  to  less  than  $15,000,000  in  1912— the  latter  figure 
being  the  smallest  since  1902.  This,  however,  is  not  to  be  criticised 
too  severely,  since  it  is  clear  that  a  continuous  expansion  in  pro- 
ductive capacity  might  easily  outrun  the  normal  consumptive  demand. 

Curve  9  represents  the  extent  to  which  surplus  earnings  have 
been  "ploughed  back"  into  the  property.  This  tells  how  the  water 
has  been  squeezed  out  of  the  common  stock.  The  report  of  the  Bureau 
of  Corporations  in  1912  shows  that,  whereas  there  was  a  capitalization 
over  indicated  investment  amounting  to  $625,353,559  in  1902,  such 
excess  was  only  $281,051,222  in  1910.  Furthermore  the  report  expressly 
states  that  this  excess  is  not  necessarily,  nor  entirely,  "water".  Up 
to  1908,  curve  9  follows  curve  8  very  closely,  indicating  that  the  new 
construction  was  largely  paid  out  of  earnings,  and  not  capitalized. 
Since  1907,  there  has  been  a  tendency  to  finance  such  additions  by 
the  sale  of  bonds.  This  tendency,  if  not  carried  too  far,  is  not  open 
to  criticism.     One  may,  therefore,  answer  the  second  question  in  the 


CORPORATION    FINANCIAL    REPORTS 


317 


Dollars 
lOO.  OOO.  OOO 

90, OOO, OOO 

SO, OOO,  OOO 

70, OOO, OOO 

60,000,  OOO 

50, OOO, OOO 

40, OOO,  OOO 

30, OOO,  OOO 

20, 000,  000 

10, 000,  000 


'02    '03    '04   '05    '06    '07    '08   '09    '10     '11     '12 

Fig.  226.    The  Maintenance  of  Property  by  the  United  States  Steel  Corporation 

Curve  7.     Depreciation,  repairs,  etc. 

Curve  8.     Expenditure  for  new  construction 

Curve  9.     Appropriation  from  surplus  earnings  for  construction  and  betterments 

No  more  lines  or  figures  are  placed  on  this  chart  than  are  really  necessary.  The  intention  was  to  make  the 
chart  just  as  simple  and  clear  as  possible.  Note  the  large  quantities  expressed  by  the  numbers  in  the 
vertical  scale,  yet  the  wide  spacing  of  the  groups  of  three  figures  makes  interpretation  very  easy 


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318 

DOLLARS 

400,  OOO,  OOO 

380,  OOO,  OOO 

360, OOO,  OOO 

340, OOO,  OOO 

320, OOO,  OOO 

300,  OOO,  OOO 

280, OOO,  OOO 

260, OOO,  OOO 

240, OOO,  OOO 

220, OOO,  OOO 

200, OOO,  OOO 

180, OOO,  OOO 

160,  OOO,  OOO 

140,  OOO,  OOO 

120.  000,  OOO 

lOO,  OOO,  OOO 

80,  OOO,  OOO 

60,  OOO,  OOO 

40,  OOO,  OOO 

20,  OOO,  OOO 


'02  '03  '04  '05  '06  '07  '08  '09  'lO  'II  '12 

Fig.  227.    Financial  Condition  of  the  United  States  Steel  Corporation  in  Different 
Years  as  Shown  by  the  Balance  Sheet 

Curve  10.     Current  assets 

Curve  11.     Cash  holdings 

Curve  12.     Current  liabilities 

Here  the  numbers  in  the  vertical  scale  represent  larger  quantities  than  in  Fig.  226  and  the  spacing  is  closer 
in  the  vertical  direction.  Nevertheless,  the  numbers  are  easily  read.  To  avoid  any  chance  of  error 
in  interpretation  it  seems  well  to  write  out  in  full  even  the  large  numbers  necessary  here 

affirmative,  for  from  the  evidence  given,  the  property  has  been  ade- 
quately maintained. 

Fig.  227  illustrates  the  financial  condition  of  the  company  as  dis- 
closed by  the  balance  sheet.  This  chart  is  very  conclusive,  for  it 
shows  a  very  large  excess  of  current  assets  over  current  liabilities, 
while  cash  holdings  have  tended  to  equal  or  exceed  the  total  cur- 
rent liabilities.  The  balance  sheet,  therefore,  indicates  continuous 
and  increasing  financial  strength.    Current  assets  in  1912  reach  nearly 


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CORPORATION    FINANCIAL    REPORTS  319 

$300,000,000,  compared  with  $275,000,000  in  1907.  Current  liabilities 
were  $60,000,000  in  1912  and  $45,000,000  in  1907,  but  cash  increased 
from  $54,000,000  to  $67,000,000.  The  Steel  stockholder  has,  therefore, 
good  evidence  that  his  comparny  is  being  managed  with  great  sagacity 
in  all  departments. 

An  exhaustive  study  of  the  United  States  Steel  Corporation  would 
require  a  great  many  charts  similar  to  the  foregoing,  but  those  given 
probably  bring  out  clearly  the  main  results  in  each  annual  report. 
The  use  of  graphics  to  drive  home  statistics  is  yet  in  its  infancy,  and 
the  next  few  years  will  doubtless  witness  a  rapidly  growing  employ- 
ment. There  seems  no  good  reason  why  any  management,  desiring 
to  tell  the  whole  truth  to  its  stockholders,  should  not  adopt  graphic 
methods  to  supplement,  as  well  as  to  illuminate,  the  statistical  tables. 

The  famous  economist,  Stanley  Jevons,  wrote  in  1875: 

There  is  much  to  be  learnt  about  money  before  entering  upon  those  abstruse 
questions,  which  barely  admit  of  decided  answers.  In  studying  a  language,  we  begin 
with  the  grammar  before  we  try  to  read  or  write.  In  mathematics,  we  practice  our- 
selves in  simple  arithmetic  before  we  proceed  to  the  subtleties  of  algebra  and  the 
differential  calculus.  But  it  is  the  grave  misfortune  of  the  moral  and  political  sciences, 
as  well  shown  by  Mr.  Herbert  Spencer  in  his  "Study  of  Sociology,"  that  they  are 
continually  discussed  by  those  who  have  never  labored  at  the  elementary  grammar 
or  simple  arithmetic  of  the  subject. 

To-day,  everyone  still  believes  himself  competent  to  discuss  cor- 
poration finance,  which  is  a  branch  of  political  science,  in  the  same 
cheerful  ignorance  of  the  fundamentals  of  the  subject.  Everything, 
therefore,  which  will  help  to  throw  light  on  the  dark  corners  of  finance 
and  make  ignorance  less  excusable  should  be  welcome.  Never  have 
corporation  managers  been  more  sensitive  to  public  opinion,  and  if 
charts  in  annual  reports  make  the  truth  more  easily  grasped  (which 
they  do)  they  will  soon  command  an  established  place  in  corporation 
records. 

This  chapter  is  largely  based  on  an  article  prepared  at  the  suggestion  of  the  author  by 
Mr.  Pierpont  V.  Davis,  of  New  York  City,  and  published  by  Mr.  Davis  in  Moody  s 

Magazine. 


320 


GRAPHIC    METHODS 


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Chapter  XVI 
GENERAL  METHODS 

THERE  are  a  number  of  comparatively  little  known  short  cuts 
and  convenient  methods  available  in  the  collection  and  record- 
ing of  statistical  facts.  If  obsolete  or  unsuitable  methods  are 
used  it  may  make  a  difference  between  success  and  failure  in  the  w  ork 
of  keeping  records  of  any  complex  business.  When  the  methods  of 
tabulation  are  too  laborious,  not  only  are  the  records  so  extensive  as 
to  be  in  disfavor,  but  they  may  occasionally  include  errors,  in  spite  of 
the  greatest  care  that  can  be  taken  by  even  the  highest  grade  of  employ- 
ees. Anything  which  will  reduce  the  amount  of  mental  concentration 
necessary  on  the  part  of  persons  collecting  and  tabulating  facts,  will 
ordinaril}'  assist  in  the  production  of  more  accurate  final  results.  In 
large  statistical  studies,  such  as  are  made  by  the  United  States  Census 
Office,  it  would  be  practically  impossible  to  get  all  the  information 
now  obtained  if  tabulating  machinery  were  not  brought  to  the  aid  of 
the  human  brain  and  hand. 

The  punched-card  system  now  widely  used  in  statistical  work  has 
made  possible  an  almost  unlimited  amount  of  subdivision  of  analysis 
with  very  little  extra  expense.  Fig.  228  shows  the  card  used  by  the 
United  States  Census  Office  for  the  1910  census.  One  of  these  cards 
was  punched  for  each  inhabitant  in  the  United  States  in  accordance 
with  the  data  obtained  by  the  Census  enumerators.  It  will  be  noticed 
that  the  card  contains  different  columns  of  names  or  numbers  and  that 
there  are  twelve  classifications  possible  in  each  vertical  column  in  which 
a  punched  hole  may  be  made.  Ordinarily  the  different  columns  are 
used  for  different  subjects,  and  the  position  of  the  punched  hole  in  each 
column  records  the  classification  of  the  data  relating  to  that  particular 
subject. 

The  punched  cards  are  stacked  so  that  all  are  right-side  up.  It  will 
be  noticed  from  Fig.  228  that  the  lower  right-hand  corner  of  the  card 

321 


322 


GRAPHIC    METHODS 


is  clipped  off.  If  any  card  in  the  stack  is  arranged  improperly,  it  will 
show  because  the  card  will  project  beyond  the  other  cards  at  the  clipped 
corner  of  the  pile.  The  stacks  of  cards  are  run  through  a  sorting  ma- 
chine such  as  is  seen  in  Fig.  229.  Needles  connected  to  electric  wires 
make  a  contact  through  the 
holes  in  the  card,  and  operate 
the  sorting  mechanism  auto- 
matically in  such  manner  that 
the  cards  are  dropped  into  com- 
partments in  accordance  with 
the  position  of  the  punched  hole 
on  the  card.  Cards  are  sorted 
for  one  particular  characteristic 
at  a  time,  so  that  all  cards 
having  that  characteristic  are 
obtained  for  tabulating  pur- 
poses. After  the  data  on  one 
set  of  cards  have  been  tabulated, 
the  cards  can  then  be  run 
through  the  sorting  machine 
again  and  sorted  for  other  char- 
acteristics. This  permits  using 
the  punched  cards  over  and 
over  again  until  all  of  the  differ- 
ent data  which  may  be  of 
interest  have  been  taken  from 
the  cards  by  the  tabulating 
machines. 

Fig.  230  shows  the  tabu- 
lating machine  as  used  in  the 
general  commercial  work 
of  corporations,  and  for 
State  or  municipal  departments. 
The  cards  are  placed  in  the  ma- 
chine at  the  left  and  are  fed 
through  automatically,  one  by  one,  so  that  electric  contacts  are  made 
wherever  there  are  holes  punched  in  the  card.  The  electric  contacts 
cause  the  counting  dials  to  revolve  by  just  the  right  amount  to  record 
properly  the  data  for  each  punched  hole. 


Fig. 


Courtesy  of  the  Tabnlating  Machine  Company 

229.  Hollerith  Card-Sorting  Machine 
Suitable  for  Use  by  Corporations  for 
Statistical  Work  Relating  to  Sales, 
Costs,  Etc. 

This  machine  will  sort  about  12,000  cards  per  hour, 
and  place  in  the  right  compartment  all  cards  having 
the  hole  punched  in  the  same  position  in  the  particu- 
lar column  for  which  the  sorting  is  done 


GENERAL   METHODS 


323 


After  any  group  of  cards  has  been  run  through  the  machine  the 
totals  can  be  read  off  from  the  counting  dials  and  written  down  by 
the  operator.  Then  the  machine  is  ready  for  some  other  set  of  cards. 
Machines  are  built  with  different  numbers  of  counting  heads  to  suit 
the  complexity  of  the  data  in  any  kind  of  business.  By  having  several 
counting  heads  on  the  same  machine,  different  sets  of  information  may 
be  taken  from  the  cards  simultaneously,  thus  frequently  permitting 
one  run  of  the  cards  through  a  tabulating  machine  to  give  all  the  data 

which   may  be   re- 
quired. 

The  punched- 
card  machines  are 
proving  to  be  of 
very  great  useful- 
ness in  commercial 
work.  Fig.  231  gives 
a  view  of  a  com- 
pletely equipped 
office  for  the  use 
of  the  punched-card 
system  by  an  elec- 
tric lighting  com- 
pany. The  data  are 
transferred  from  the 
original  records  to 
the  cards  by  very 
simple  punching 
machines  with  keys 
somewhat  similar 
to  typewriter  keys.  The  punching  is  usually  done  by  girls.  A  little 
training  and  practice  gives  high  speed.  Once  punched,  the  cards  are 
always  available  and  may  be  filed  for  record  purposes.  It  is  frequently 
a  great  convenience  to  be  able  to  run  through  the  machines  cards  for 
several  years  back  so  that  comparative  statistics  may  be  made.  The 
preservation  of  the  cards  makes  it  unnecessary  to  dig  out  the  original 
records.  The  uniform  size  of  the  cards  makes  it  possible  to  preserve 
large  quantities  of  them  with  comparatively  little  labor. 

In  punching  the  cards  there  are  certain  holes  relating  to  depart- 
ments, dates,  etc.,  which  are  repeated  time  after  time  for  large  numbers 


•.'otiilesy  of  the  Tabulating  Machine  Company 

Fig.  230.     Hollerith  Tabulating  Machine  for  Totalling 
the   Data  Contained  on  Punched   Cards 

The  machine  illustrated  has  four  counters,  permitting  the  simulta- 
neous taking  off  of  the  data  contained  under  four  different  headings 
on  the  punched  card.  The  sorted  cards  are  placed  at  the  left 
of  the  tabulating  machine  and  run  through  at  the  rate  of  about 
3,000  per  hour.     Totals  are  read  from  the  dials  shown  at  the  right 


324  GRAPHIC    METHODS 

of  cards.  Instead  of  the  operators  punching  these  repeated  holes  one 
by  one  in  each  card,  the  cards  are  punched  by  a  gang  punch,  which  at  a 
single  stroke  punches  several  holes  in  many  different  cards.  The  gang 
punch  can  be  seen  in  Fig.  231  on  a  table  near  the  right-hand  side  of  the 
illustration. 

Manufacturing  companies  now  use  the  tabulating  machines  for 
keeping  track  of  the  cost  of  different  orders  and  of  different  classes 
of  work  in  the  factory.  The  data  from  the  original  time  slips  of  the 
workmen  are  transferred  by  the  punching  machines  to  the  cards  day 
by  day  as  the  time  slips  are  turned  in.  The  punched  cards  can  then  be 
sorted  by  order  number  and  department,  so  that  when  each  order 
is  completed  the  total  cost  of  all  work  on  that  order  is  obtained.  The 
distribution  of  the  value  of  work  done  by  different  departments  can  be 
had  also  if  desired. 

In  keeping  the  records  of  a  sales  department,  the  facts  relating 
to  the  various  sales  orders  are  transferred  to  the  punched  cards  and  the 
cards  sorted  and  tabulated  in  any  manner  desired.  A  very  large  manu- 
facturing business  having  many  kinds  of  machinery  as  a  product,  uses 
the  punched-card  system  for  each  order  as  it  is  received  in  the  plant. 
At  the  end  of  each  month  the  records  show  the  total  sales  of  each  branch 
house,  the  total  sales  of  each  salesman,  the  total  sales  of  each  main  class 
of  product,  and  many  other  kinds  of  information.  In  this  particular 
plant  tabulating  machines  are  of  very  great  assistance,  because  they 
can  be  used  to  make  a  sales  analysis  for  any  one  class  of  product.  The 
punched  card  for  each  order  shows  the  catalogue  number  of  the  product 
called  for  by  that  order.  Whenever  desired,  cards  for  a  definite  length 
of  time  can  be  run  through  the  machines  so  as  to  sort  out  all  the  cards 
for  any  catalogue  number  of  product  on  which  a  study  is  to  be  made. 
The  resorting  of  these  cards  by  sales  districts  shows  the  distribution 
of  the  total  sales  of  this  particular  product  by  distinct  districts,  or 
States,  and,  if  desired,  by  different  salesmen.  The  sales  for  the  various 
months  or  seasons  of  the  year  may  be  had  if  wanted.  Though  the  data 
relating  to  the  many  kinds  of  product  need  not  be  regularly  tabulated, 
the  facts  are  nevertheless  preserved  so  that  tabulation  for  any  particular 
class  of  goods  or  any  territory  can  be  made  whenever  a  study  seems 
desirable. 

The  multitudinous  uses  to  which  these  card-sorting  and  tabulating 
machines  can  be  put  are  far  beyond  any  possibility  of  naming  here. 
The  very  great  flexibility,  speed,  and  accuracy  of  the  machines  make 


J 


GENERAL   METHODS 


325 


Courtesy  of  the  Tabulating  Machine  Comvany 

Fig.  231.    A  Completely  Equipped  Office  for  Collecting  and  Tabulating  the  Operating 
and  Sales  Statistics  of  an  Electric-Lighting  Company 

The  girls  at  the  left  are  operating  the  key  punches  for  punching  the  cards.  A  gang  punch  is  shown  on 
the  table  at  the  extreme  right.  In  the  corner  is  the  card-sorting  machine,  and  the  tabulating  machine 
is  in  the  center.     Files  for  punched  cards  are  seen  along  the  wall 

them  almost  indispensable  in  any  work  where  there  is  large  quantity 
of  complex  data  to  be  analyzed.  It  has  been  found  feasible  and  profit- 
able to  use  machines  of  this  type  in  businesses  of  only  moderate  size. 
The  adding  machine  is  now  so  commonly  used  that  it  seems  scarcely 
worth  while  to  mention  it  here.  There  are,  however,  frequently  times 
when  special  investigations  must  be  made,  but  adding  machines  do 
not  happen  to  be  available,  and  the  investigator  feels  seriously  handi- 
capped because  he  must  take  from  the  original  records  only  those 
items  which  may  be  of  especial  interest  to  him.  In  work  of  this  kind, 
it  is  sometimes  convenient  to  use  one  of  the  small-size  pocket  adding 
machines  of  which  there  are  several  different  makes  now  on  the  mar- 
ket. Though  these  machines  are  not  at  all  in  the  same  class  as  the 
large  key-operated  machines,  they  are  of  assistance  in  taking  off 
occasional   items   because   they   overcome   the   necessity   for   putting 


326  GRAPHIC    METHODS 

down  the  items  on  a  piece  of  paper  for  addition  later  by  mental  effort. 
With  the  portable  adding  machine  the  data  are  taken  from  the  original 
work  directly  and  added  automatically  as  the  work  proceeds. 

Engineers  do  the  greater  portion  of  all  of  their  computing  work 
by  means  of  the  slide  rule.  By  others  than  engineers,  however,  the 
slide  rule  is  very  little  used.  In  the  preparation  of  data  for  curves 
and  charts  for  corporation  work,  or  for  any  investigations  where 
numerous  percentages  are  necessary,  the  slide  rule  is  almost  indispen- 
sable. A  10-inch  slide  rule  as  shown  in  Fig.  232  is  sufficiently  accurate 
for  most  work,  and,  as  it  costs  only  a  few  dollars,  it  should  be  a  part 
of  the  equipment  of  everyone  who  is  doing  even  the  simplest  form  of 
statistical  work,  or  who  is  periodically  plotting  curves  involving 
ratios  or  percentages.  By  using  a  slide  rule  the  percentage  ratios  of 
numbers  can  be  determined  almost  instantly  and  with  no  mental 
effort.  It  can  be  confidently  predicted  that  anyone  who  has  much 
multiplication  or  division  to  do  in  relation  to  curve-plotting  and  chart- 
making  will  find  the  slide  rule  of  such  a  great  assistance  that  the 
rule  would  not  be  parted  with  under  any  circumstances  if  a  new  one 
could  not  be  obtained. 


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Fig.  232.    A  lo-inch  Slide  Rule 

The  slide  rule  is  of  great  convenience  in  doing  work  involving  multiplication  or  division- 
It  is  especially  valuable  for  obtaining  ratios  or  percentages  in  statistics  for  industrial 
work 

Judgment  must  be  used  in  the  showing  of  figures  in  any  chart 
or  numerical  presentation,  so  that  the  figures  may  not  give  an  ap- 
pearance of  greater  accuracy  than  their  method  of  collection  would 
warrant.  Too  many  otherwise  excellent  reports  contain  figures  which 
give  the  impression  of  great  accuracy  when  in  reality  the  figures  may 
be  only  the  crudest  approximations.  Except  in  financial  statements, 
it  is  a  safe  rule  to  use  ciphers  whenever  possible  at  the  right  of  all 
numbers  of  great  size.  The  use  of  the  ciphers  greatly  simplifies  the 
grasping  of  the  figures  by  the  reader,  and,  at  the  same  time,  it  helps 
to  avoid  the  impression  of  an  accuracy  which  is  not  warranted  by 
the  methods  of  collecting  the  data. 

A  recent  government  report*  contained  this  statement:  "The 
cotton    crop    of   last   year    (1911)    aggregated    16,250,276    500-pound 

*  "The  Packing  and  Marketing  of  Cotton,"  by  John  M.  Carson. 


GENERAL   METHODS  327 

bales,  the  total  value  of  which  is  $1,000,000,000  and,  including  the  seed, 
$1,200,000,000."  The  figure  for  the  number  of  bales  imphes  that 
every  single  bale  of  cotton  raised  in  the  United  States  was  accounted 
for  and  that  these  figures  are  absolutely  accurate  down  to  one  bale  of 
cotton.  This  denotes  an  accuracy  of  1  part  in  16,000,000  parts,  or  an 
accuracy  within  0.000006  per  cent.  It  is  very  doubtful  indeed  whether 
the  figures  for  the  cotton  crop  are  accurate  within  1,000  or  even  10,000 
bales.  Suppose  a  possible  error  of  10,000  bales  were  assumed,  and  the 
cotton  crop  put  down  as  16,250,000  bales,  the  accuracy  would  still 
be  1  in  1,625,  or  within  0.06  per  cent.  For  most  purposes  it  would 
be  much  preferable  to  use  the  round  number  16,250,000  instead  of  the 
detailed  figures  which  were  given  in  the  Government  report.  The 
particular  report  from  which  the  figures  are  taken  is  not  a  tabulation, 
but  a  written  report  in  regard  to  the  methods  used  for  packing  cotton. 
Since  the  report  was  intended  to  be  read  by  merchants  and  planters, 
rather  than  by  statisticians,  it  is  all  the  more  important  that  the 
figures  should  be  presented  in  round  numbers  so  that  they  may  be 
easily  grasped.  The  mere  fact  that  values  for  the  cotton  in  the  latter 
part  of  the  quotation  given  above  are  in  very  rough  estimates  of  such 
round  numbers  as  "$1,000,000,000",  calls  special  attention  to  the 
use  of  detailed  figures  for  the  "16,250,276  bales". 

Misleading  figures  implying  a  greater  accuracy  than  justifiable 
are  very  often  found  as  a  result  of  the  addition  of  different  quantities 
some  of  which  are  large  and  some  small.  The  small  quantities  may 
have  a  great  degree  of  accuracy,  but  this  does  not  give  accuracy  to 
the  sum  of  all  the  quantities,  for  the  total  cannot  be  any  more  accu- 
rate than  the  most  inaccurate  item  included  in  the  total.  If  a  very 
large  item  is  not  accurate  within  ten  thousand,  then  it  is  useless  to 
include  in  the  grand  total  the  three  right-hand  digits  which  may  be 
obtained  as  the  result  of  addition.  When  some  of  the  items  included 
are  so  small  that  they  are  in  tens  or  hundreds,  the  addition  should  be 
made  to  include  all  the  digits.  After  the  sum  is  known  then  all  those 
digits  whose  accuracy  is  doubtful  in  the  total  should  be  replaced  by 
ciphers. 

Fictitious  accuracy  is  quite  often  implied  in  the  results  of  com- 
putations where  a  slide  rule  has  been  used.  The  ordinary  10-inch 
slide  rule  can  give  an  accuracy  of  only  three  significant  figures,  and, 
on  the  right-hand  portion  of  the  scale,  the  third  figure  is  often  some- 
what in  doubt  unless  very  great  care  is  used  in  manipulating  the 


S28  GRAPHIC    METHODS 

rule.  This  means  that  with  the  10-inch  shde  rule  the  accuracy  is 
ordinarily  no  greater  than  1  in  1,000,  or  one-tenth  of  one  per  cent. 
Though  two  quantities  each  running  into  five  figures  may  be  multi- 
plied on  the  slide  rule,  the  product  would  not  be  accurate  beyond  three 
/•significant  figures,  and  ciphers  must  be  put  down  to  express  the  re- 
mainder of  the  number  for  the  product. 

If  very  large  quantities  obtained  by  slide-rule  computation  are 
added  together  with  a  number  of  small  quantities,  the  total  cannot, 
of  course,  be  accurate  beyond  the  third  or  fourth  digit  toward  the  right 
of  the  largest  quantity  included  in  the  total.  The  fourth  digit  may  be 
fairly  accurate  in  the  total,  because  in  the  process  of  addition  the 
various  figures  added  would  tend  to  give  a  close  approximation  of  the 
fourth  digit  and  that  digit  might  accordingly  be  put  down  in  the  total 
because  it  has  at  least  a  fair  possibility  of  accuracy. 

It  must  not  be  assumed  from  the  preceding  paragraph  that  the  slide 
rule  gives  figures  too  crude  for  ordinary  use.  There  are  comparatively 
few  sets  of  data  relating  to  costs,  output,  or  other  records  of  industrial 
work  which  have  an  accuracy  greater  than  one-ten.th  of  one  per  cent. 
For  the  great  majority  of  ordinary  problems,  the  data  are  so  crude  that 
the  10-inch  rule  has  more  than  sufficient  accuracy.  The  use  of  the 
slide  rule  on  many  classes  of  work  has  a  desirable  psychological  effect, 
in  that  it  calls  attention  to  the  accuracy  of  the  data  and  assists  in  pre- 
venting unnecessary  detail  work  which  it  is  very  easy  to  drift  into  if 
any  assumptions  of  great  accuracy  are  permitted  to  creep  in. 

The  question  of  significant  figures  in  statistical  work  and  even  in 
ordinary  commercial  reports  is  an  important  one  which  should  have 
greater  attention  than  it  ordinarily  receives.  Unfortunately  the  sub- 
ject can  be  only  briefly  touched  upon  here  and  the  reader  would  do  well 
to  look  the  matter  up  in  some  of  the  books  on  statistical  theory.* 

It  sometimes  happens  that  a  few  blue  prints  are  required  from 
some  complex  chart  made  on  heavy  paper  or  cardboard.  Instead  of 
making  a  tracing  from  the  drawling  by  means  of  tracing  cloth  and  with 
great  expenditure  of  labor  and  time,  it  is  sometimes  feasible  to  treat 
the  original  drawing  with  a  transparentizing  solution  so  that  blue 
prints  can  be  obtained  directly.  The  transparentizing  solution  is  put  on 
the  paper  with  a  brush  or  sponge  and  then  blue  prints  are  made  in  the 
ordinary  manner.     There  are  several  different  makes  of  the  trans- 

*  A  chapter  on  "  Approximation  and  Accuracy  "  will  be  found  in  "  The  Elements  of  Statistical  Method,"  by  Willford  I.  King, 
published  by  the  MacmiUan  Company,  New  York  City. 


GENERAL   METHODS  329 

parentizing  solution  on  the  market  and  a  supply  can  be  obtained  from 
most  shops  selling  drafting  materials. 

During  the  last  few  years  very  convenient  photographic  machines 
have  been  put  on  the  market  which  photograph  directly  on  sensitized 
paper  without  the  use  of  any  negative.  With  this  type  of  machine, 
copies  of  drawings  can  be  made  very  cheaply  and  clearly.  One  of  the 
convenient  features  in  doing  work  by  this  machine  is  that  drawings 
can  be  enlarged  or  reduced  within  a  wide  range  of  sizes.  The  machine 
most  commonly  used  for  this  work  is  called  the  photostat.  In  most 
large  cities  there  are  companies  equipped  with  the  photostat  appara- 
tus who  w^ill  at  reasonable  cost  make  copies  of  drawings  sent  to  them, 
much  as  the  blue-printing  companies  make  copies  from  tracings.  Some 
of  the  best  equipped  libraries  have  now  installed  photostat  machines 
as  a  convenience  to  their  patrons.  In  a  library  so  equipped  it  is  pos- 
sible to  have  a  copy  made  from  any  page  in  any  book  or  periodical  in 
the  library.  In  the  New  York  Public  Library,  the  reader  need  only 
fill  out  an  order  form  giving  the  exact  page  and  the  name  of  the  publica- 
tion from  which  the  copy  is  to  be  made,  and  state  the  size  desired  in  the 
reproduction.  Usually  the  copy  is  available  within  a  few  hours,  but, 
if  desired,  it  may  be  mailed,  thus  avoiding  any  necessity  for  waiting 
on  the  part  of  the  person  ordering  the  copy.  In  case  of  rare  books  or 
manuscripts,  copies  may  be  made  page  by  page  so  that  a  complete  copy 
of  the  book  is  obtained  without  prohibitive  expenditure. 

Charts  from  which  plates  must  be  made  for  printing  are  nearly 
always  drawn  considerably  larger  in  size  than  the  completed  illustration. 
Most  of  the  charts  in  this  book  were  drawn  two  or  three  times  as  large 
as  seen  here.  A  photographic  reduction  in  the  size  of  the  chart  tends  to 
eliminate  minor  irregularities  and  gives  a  much  better  result  than  can 
possibly  be  obtained  from  drawings  in  the  exact  finished  size.  In 
making  the  original  large-size  drawings  it  is  almost  essential  that  a 
reducing  glass  should  be  used  to  make  certain  that  the  finished  drawing 
will  have  the  desired  appearance.  With  complex  drawings  it  is  often 
difficult  to  tell  whether  the  lettering  and  figures  are  of  large  enough  size 
to  be  read  easily  after  they  are  reduced  to  the  size  to  be  used  for  print- 
ing. By  looking  through  a  reducing  glass  it  can  be  determined  at 
once  whether  the  drawing  is  in  correct  proportions.  A  reducing  glass 
is  similar  in  appearance  to  the  ordinary  magnifying  glass,  but  the  lens 
is  ground  concave  instead  of  convex  so  that  everything  seen  through 
the  glass  appears  of  smaller  size.     The  ordinary  reducing  glass  can  be 


330  GRAPHIC    METHODS 

used  for  a  reduction  through  quite  a  range  of  different  sizes  by  holding 
the  glass  at  different  distances  from  the  drawing  which  is  being  con- 
sidered. 

One  of  the  commonest  errors  made  by  the  beginner  in  preparing 
charts  from  which  printing  plates  are  to  be  made  is  that  he  does  not 
allow  for  the  reduction  in  widths  of  the  various  lines.  If  the  printing 
plate  is  to  be  made  one-third  the  lineal  dimension  of  the  original  draw- 
ing, it  is  essential  that  the  lines  on  the  original  drawing  should  be  made 
three  times  as  wide  as  they  are  to  appear  when  printed.  The  novice 
will  find  that  even  though  he  uses  a  reducing  glass  with  great  care,  his 
heavy  lines  will  at  first  nearly  always  appear  less  wide  and  black  than 
he  had  expected  and  hoped  that  they  would  be. 

Quite  often  it  is  desired  to  change  the  proportions  of  some  chart 
so  that  the  ratio  between  height  and  width  may  be  different  from  that 
of  the  original  drawing.  Though  the  photographic  process  used  in 
the  photostat  machine  or  by  the  engraver  (in  making  plates  for  print- 
ing) permits  a  change  in  size,  the  same  proportions  remain  between 
width  and  height.  There  would  seem  to  be  enough  demand  to  justify 
an  engraver  making  a  combination  of  lenses  by  which  one  dimension 
of  a  drawing  may  be  changed  more  than  the  other  dimension.  By 
using  two  lenses  having  cylindrical  surfaces  and  having  the  axes  at 
right  angles,  there  might  be  a  possibility  of  changing  the  proportions 
of  drawings  which  are  copied  without  any  great  amount  of  expense 
after  the  apparatus  has  once  been  designed. 

Very  often  persons  owning  cameras  do  not  know  that  the  camera 
manufacturers  are  in  many  cases  able  to  supply  auxiliary  lenses  by 
which  pictures  and  copies  of  drawings  may  be  made  practically  full- 
size  with  ordinary  cameras.  Though  the  arrangement  is  not  as  con- 
venient to  use  as  a  regular  copying  camera,  it  may  be  of  great  service 
to  supplement  the  work  of  a  camera  already  owned. 

It  is  not  generally  known  that  line  plates  may  be  made  from  charts 
drawn  on  co-ordinate  paper  ruled  with  green  ink.  Such  charts  sent 
to  many  zinc  engravers  are  returned  with  the  statement  that  it  is 
impossible  to  make  a  line  cut  from  green-ink  copy.  The  statement 
is  made  in  most  cases  by  the  engraver  without  even  attempting  to 
make  the  cut.  There  is  no  difficulty  in  making  excellent  zinc  cuts 
from  copy  using  the  ordinary  green  ink,  and  many  of  the  cuts  in  this 
book  have  been  so  made,  as,  for  instance.  Fig.  156,  Fig.  207,  and 
Fig.  215. 


GENERAL   METHODS  331 

Of  course,  when  line  cuts  are  made  from  charts  having  a  green-ink 
background,  the  printed  ilkistration  shows  both  the  black  and  green- 
ink  lines  as  black,  and  there  is  no  distinction  between  the  different 
lines.  On  this  account,  it  is  necessary  for  the  person  ordering  the 
charts  made  from  paper  having  green-ink  lines  to  make  certain  that 
the  main  features  of  the  chart  stand  out  with  prominent  broad  lines, 
so  that  there  may  certainly  be  a  contrast  in  the  width  of  the  lines 
when  printed,  to  make  up  for  the  contrast  obtained  in  the  original 
drawing  by  the  difference  in  color  of  the  two  inks  used. 

Color  printing  is  not  yet  ordinarily  available  unless  a  very  large 
number  of  copies  are  to  be  made.  In  order  to  make  areas  stand  out 
in  contrast,  different  kinds  of  cross-hatching  put  on  by  hand  ruling 
have  been  used  very  commonly.  One  trouble  with  the  hand  ruling 
is  that  it  lacks  uniformity  unless  done  with  very  great  care  and  to  a 
scale  considerably  larger  than  the  finished  illustration,  so  that  there 
may  be  enough  photographic  reduction  to  eliminate  many  of  the  de- 
fects which  would  otherwise  appear.  It  is  not  widely  known  that 
there  is  a  method  available  in  the  form  of  Ben  Day  mechanical  shading, 
which  is  far  superior  to  cross-hatching  for  line-plate  work.  Most 
good  engravers  can  do  Ben  Day  work,  and  it  is  just  a  matter  of  speci- 
fying what  kind  of  shading  is  desired  on  the  different  portions  of  the 
drawing.  With  the  Ben  Day  shading,  more  degrees  of  shading  from 
light  to  dark  are  feasible  than  with  hand  work,  and,  in  addition,  there 
are  many  varieties  of  lines  and  patterns  which  may  be  used. 

Since  Ben  Day  work  must  be  applied  on  each  area  separately  by 
means  of  a  transfer  process,  it  is  necessary  for  the  engraver  to  make 
certain  that  the  Ben  Day  shading  shall  not  appear  on  some  portion 
of  the  zinc  plate  where  it  is  not  desired.  This  requires  that  the  en- 
graver must  protect  the  different  portions  of  the  zinc  plate  by  a  paint- 
like covering,  and  this  must  be  done  for  each  of  the  different  kinds  of 
shading  used.  It  is  almost  impossible  to  make  any  square-inch  price 
rate  for  Ben  Day  work  because  each  new  plate  is  a  problem  in  itself. 
The  work  is  ordinarily  charged  for  on  a  time  basis,  the  usual  rates 
being  from  $1.00  to  $1.50  per  hour. 

When  copy  to  receive  Ben  Day  work  is  sent  to  the  engraver  it 
is  marked  somewhat  as  shown  in  Fig.  233,  so  that  the  instructions 
to  the  engraver  may  be  explicit.  Crayon  marks  specify  by  number 
the  kind  of  Ben  Day  shading  desired,  and  arrows  point  to  the  different 
areas  to  be  shaded.    This  marking  of  instruction  is  done  with  a  blue 


332 


GRAPHIC    METHODS 


pencil  because  blue  does  not  photograph  easily  and  has  such  a  small 
effect  on  a  photographic  plate  that  it  does  not  spoil  the  copy  for  making 
a  good  zinc  plate.  In  order  to  make  the  zinc  plate  from  which  Fig. 
233  was  actually  printed,  a  red  pencil  was  used  for  the  bottom  portion 
of  the  illustration  referring  to  Ben  Day  work.  Red  photographs  as 
black,  and  a  zinc  plate  was  obtained  which  shows  the  marking  such 
as  would  be  used  with  a  blue  pencil  when  Ben  Day  work  is  ordered 
from  an  engraver.  Ben  Day  work  has  been  used  on  a  great  many  illus- 
trations in  this  book,  and  it  is  believed  that  the  reader  will  have  no 
difficulty  in  distinguishing  the  cuts  with  Ben  Day  work  from  those 
cuts  for  which  hand  shading  was  used. 


(0       w 
6  .    b 


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(0 

<0 

o 

0) 

»• 

t^ 

_ 

ID 

•«t 

(U 

CO 

^ 

ii) 

0) 

iD 

N 

(D 

(0 

■* 

(0 

o 

cu 

C) 

(0 

H- 


vX^W^Iv^ 


fi. 


Fig*  233.     Copy  from  Which  a  Zmc  Plate  Is  to  Be  Made  with  Ben  Day  Mechanical 

Shading 

This  is  the  copy  from  which  the  plate  for  Fig.  1  was  made.  The  areas  to  receive  the  Ben  Day  work  are 
designated  by  arrows  and  numbers  naming  the  particular  kind  of  shading  desired.  Sample  books  give 
a  wide  choice  of  shadings.  The  markings  on  the  face  of  the  copy  regarding  the  Ben  Day  work  are  made 
with  blue  pencil,  since  blue  does  not  photograph  dark  enough  to  affect  the  line  engraving 


GENERAL    METHODS 


333 


There  are  a  great  many  problems  in  graphic  work  which  puzzle 
the  person  getting  up  a  chart  if  there  are  three  different  variables 
to  deal  with.  The  problem,  as  ordinarily  found,  involves  two  differ- 
ent independent  variables,  and  a  dependent  variable  depending  upon 
each  of  the  two  independent  variables.     Isometric  drawings  like  Fig. 


235,  or  solid  models  such 
as  are  seen  in  Fig.  236 
and  Fig.  237,  can  be 
used,  but  they  require  a 
great  deal  of  labor  and 
care  to  make  and  are 
accordingly  not  often 
seen.  There  is  another 
method  not  perhaps  so 
obvious  as  a  solid  model 
but  nevertheless  of  great 
value.  When  the  data 
follow  any  definite  nat- 
ural laws  a  chart  on  the 
style  of  Fig.  234  is  often  p. 
simple  to  make  and  easy 
to  interpret.  By  such 
charts  many  computa- 
tions may  be  made  with 
accuracy  and  ease. 


Wfmn  efjrm  fii/fm  ^sTMa. 


Umrn  ///  //tc//a 

CouTlesy  of  Data.  Chicago 

234.  Chart  for  Obtaining  the  Weight  of  Steel 
Plates  3^8-inch  Thick  and  of  Various  Widths  and 
Lengths 

A  chart  of  this  general  tj^pe  permits  using  three  variables.  The  two 
independent  variables  here  are  length  and  width.  Weight  is  the 
dependent  variable.  This  kind  of  chart  is  much  simpler  to 
construct  than  an  isometric  drawing  like  Fig.  167,  or  a  model  like 
Fig.  236  or  Fig.  237 

In  obtaining  curves  like  those  shown  in  Fig.  234  one  of  the  variables 
is  made  some  constant  quantity,  and  the  other  tw^o  variables  are  then 
used  to  work  out  the  data  from  which  the  curve  is  drawn.  It  can  be 
seen,  for  instance,  that  if  a  definite  weight  and  length  of  steel  plate 
Vs  inch  thick  is  assumed,  the  width  is  absolutely  fixed.  To  obtain  a 
curve  like  that  seen  for  5  pounds  in  Fig.  234,  it  is  necessary  only  to 
assume  a  weight  of  5  pounds,  then  choose  separate  lengths  one  by  one, 
and  compute  the  widths  which  w^ould  correspond  with  the  lengths 
selected  to  give  a  weight  of  5  pounds.  The  various  figures  of  width 
obtained  are  then  plotted  as  points  for  the  5-pound  curve,  and  a  smooth 
curve  is  drawn  through  all  of  the  points,  giving  the  result  seen  in  the 
illustration.  After  one  curve  has  been  plotted  another  weight  is 
assumed  in  a  similar  manner,  and  new  computations  are  made  for 
various  lengths  on  the  horizontal  scale.     Though  this  method  of  chart- 


334 


GRAPHIC    METHODS 


'«00 


ing  requires  some  little  labor  in  making  the  various  computations,  it  is 
a  very  excellent  one  where  the  chart  must  be  used  for  frequent  reference. 
The  information  from  such  a  chart  as  seen  in  Fig.  234  may  be  read  from 
any  portion  of  the  chart,  even  though  the  intersection  of  the  length  and 
width  lines  for  the  size  of  the  plate  under  consideration  does  not  fall  on 
one  of  the  curve  lines  drawn.  It  can  be  seen  for  the  example  stated  in 
the  lower  left-hand  corner  of  the  chart  that  the  intersection  of  the  ver- 
tical and  horizontal  lines  of  the  independent  variables  falls  halfway 
between   the   curve   for  20   pounds    and    the    curve    for    25    pounds. 

The  weight  is  accord- 
ingly taken  as  223^ 
pounds. 

Though  the  sub- 
ject cannot  be  fully 
gone  into  here,  it  may 
be  suggested  for  those 
who  care  to  consider 
further  the  general 
type  of  charts  repre- 
sented by  Fig.  234, 
that  much  work  may 
be  saved  by  making 
such  charts  on  loga- 
rithmic paper.  This 
subject  has  been  dis- 
cussed at  greater  length 
in  a  preceding  chapter. 
There  are  many  classes 
of  data  which,  when 
plotted  on  ordinary 
squared  co-ordinate 
paper,  involve  plotting 
234,  but 


Fig 


Data  of  Guido  H.  Marx.     Courtesy  of  the  Standard  Corporation,  Philadelphia 

235.  Relations  Between  Arc  of  Action  in  Inches, 
Pitch  Speed  in  Feei  per  Minute,  and  Breaking 
Load  in  Pounds,  for  Cut  Cast-iron  Gears  of  Ten 
Diametral  Pitch 

This  illustration  is  drawm  on  isometric  ruling,  with  the  ruling  itself 
seen  only  as  a  background  so  as  to  give  the  appearance  of  a  solid 
model  in  three  dimensions 


seen   m 


Fig. 


many  points  to  produce  curves  like  those 
for  which  the  same  data  shown  on  paper  with  logarithmic  ruling 
would  give  straight  lines.  When  the  curve  lines  are  straight  lines,  it 
is  necessary  to  plot  only  two  points  for  each  curve  and  then  draw  a 
line  connecting  those  two  points.  This  permits  a  very  rapid  construc- 
tion of  the  chart.  A  little  practice  in  the  making  of  charts  is  necessary 
before  one  can  determine  clearly  the  best  method  to  use  so  as  to  produce 


GENERAL   METHODS 


335 


a  simple  chart.  Paper  having  logarithmic  ruHng  in  both  directions  is 
the  kind  most  frequently  used  for  mathematical  charts.  Such  paper 
can  be  purchased  from  almost  any  good  store  selling  engineering  sup- 
plies. Readers  wishing  to  go  further  into  the  preparation  of  charts  of 
this  rather  highly  specialized  character  are  referred  to  the  excellent 
work  of  Mr.  John  B.  Peddle, 
entitled  "The  Construction 
of  Graphical  Charts",  pub- 
lished by  the  McGraw-Hill 
Book  Company  of  New  York 
City. 

The  use  of  isometric  pa- 
per for  drawing  charts  repre- 
senting three  dimensions 
was  mentioned  for  Fig.  167. 
In  Fig.  235  we  have  another 
application  of  this  same  iso- 
metric ruling.  Instead  of 
showing  the  whole  sheet  of 
isometrically  ruled  paper  as 
a  background,  Fig.  235  shows 
only  enough  of  the  iso- 
metric ruling  to  give  the  im- 
pression of  three  planes  meet- 
ing like  one  corner  of  a  box. 
The  chart  illustrating  the 
data  is  drawn  on  the  isomet- 
ric ruling  so  that  it  appears 
as  though  placed  in  a  corner 

made  by  the  three  planes.  Parallel  ruled  lines  then  permit  reading  the 
chart  from  any  one  of  the  three  different  scales.  The  dependent 
variable  is  made  the  vertical  scale  here,  just  as  iji  most  charts  where 
there  is  only  one  independent  variable  instead  of  two.  The  use  of  the 
isometric  ruling  is  not  as  common  as  it  would  be  if  it  were  more  widely 
realized  how  easily  charts  may  be  prepared  to  give  the  effect  of  solid 
models  without  the  great  labor  which  a  solid  model  necessarily  involves. 

Fig.  236  shows  another  method  which  may  be  used  instead  of  the 
more  laborious  and  costly  solid  model.  Different  curves  are  plotted 
by  assuming  at  frequent  intervals  constant  values  for  one  of  the  vari- 


Data  of  E.  S.  Farwell.     Courtesy  of  the  American  Machinist 

Fig.  236.  Tests  of  a  Direct-connected  Fan  and 
Engine.  The  Model  Shows  the  Effect  on  the 
Efficiency  of  the  Fan  of  Different  Outlet  Open- 
ings and  of  Different  Speeds  of  Operation 

Curves  are  plotted  on  cardboard  by  assuming  constant  values 
for  one  of  the  three  variables,  and  then  plotting  the  rela- 
tions for  the  other  two  variables.  Each  of  the  curves  is 
cut  from  the  cardboard  and  slit  halfway  up  or  do^^-n  the 
line  for  intersection  with  the  cards  at  right  angles  to  it. 
Cards  are  fitted  together  to  give  the  effect  seen  above 


336  GRAPHIC    METHODS 

ables  of  the  data,  and  then  plotting  curves  for  the  other  two  variables. 
These  curves  are  made  to  the  same  scale  on  sheets  of  cardboard,  and 
then  the  outline  of  the  curve  is  cut  out  with  shears  so  as  to  give 
a  series  of  different  cardboard  curve  sheets.  The  several  sheets  are 
carefully  marked  for  their  intersecting  points,  and  are  then  cut  half- 
way through  in  the  upward  and  downward  direction  on  the  intersection 
lines  so  that  the  curve  sheets  may  be  fitted  together  to  give  an  effect 
like  that  seen  in  Fig.  236.  A  cardboard  exhibit  on  the  scheme  of  Fig. 
236  is,  in  many  cases,  just  as  satisfactory  as  a  solid  model  and  it  has 
the  advantage  of  being  quite  easy  to  prepare  without  any  special 
apparatus  or  materials  being  required. 

Fig.  237  shows  a  solid  model  of  the  type  which  may  be  considered 
the  acme  of  graphic  work  when  there  are  two  independent  variables. 
A  model  of  this  kind  is  ordinarily  made  of  plaster  of  Paris,  as  that  is  a 
material  easily  handled  and  capable  of  being  made  into  any  shape 
desired.  In  making  such  a  model  the  usual  procedure  would  be  to 
rule  a  flat  board  with  lines  at  properly  spaced  intervals  for  each  of  the 
two  horizontal  scales.  Computations  made  by  methods  similar  to 
those  described  for  Fig.  236  would  give  the  value,  on  the  vertical  scale, 
for  each  set  of  conditions  corresponding  to  the  intersection  of  each  two 
lines  ruled  for  the  base  and  showing  the  horizontal  scales.  In  Fig.  237 
the  cost  computations  can  be  considered  to  give  points  on  curves  drawn 
on  the  surface  of  the  solid  model.  These  curves  correspond  exactly 
with  the  curves  drawn  on  cardboard  in  Fig.  236.  In  order  to  locate 
the  curve  points  which  determine  the  surface  of  a  solid  model  like  Fig. 
237,  wires  are  driven  into  the  bottom  board  at  the  intersection  of  the 
ruled  lines  of  the  two  horizontal  scales,  and  these  wires  are  made  just 
the  proper  length  to  represent  the  figures  computed  for  the  dependent 
variable.  When  all  the  wires  are  in  position  on  the  board,  a  box  is 
made  the  right  size  for  the  base  of  the  finished  solid  model,  and  with 
sides  as  high  as  the  solid  model  is  to  be  made.  This  box  serves  as  a  mold 
into  which  the  wet  piaster  of  Paris  is  poured.  Care  must  be  taken  to 
have  the  bottom  edges  of  the  box  fit  well  on  the  board  so  that  the  liquid 
plaster  of  Paris  may  not  leak  out. 

The  powdered  plaster  of  Paris  may  be  obtained  from  any  store 
selling  building  supplies,  or  from  a  drug  store.  Water  is  added  and 
the  mixture  carefully  stirred  until  it  is  free  from  lumps  and  of  about 
the  consistency  of  very  thick  cream.  The  fluid  is  poured  into  the 
box  up  to  the  desired  height  and  allowed  to  stand  for  several  hours 


GENERAL   METHODS 


337 


or  over  night  until  it  becomes  thoroughly  hard.  The  box  is  then 
removed.  In  order  to  get  the  shape  of  the  model  as  seen  in  Fig.  237, 
the  plaster  of  Paris  is  very  carefully  scraped  away  with  a  piece  of 
tin  or  some  other  simple  tool  until  the  ends  of  the  vertical  wires  just 
show  through.  Before  the  plaster  of  Paris  is  poured  in,  care  should 
be  taken  to  mark  the  different  sides  of  the  board  so  that  it  will  be 


R.  E.  Scott,  in  Harvard  Engineering  Journal 


Fig. 


237.  Three-dimensional  Model  Showing  Cost  of  Light  in 
Cents  per  1,000  Candle-hours  with  40-watt  "Mazda"  Lamps 
for  Any  Practicable  Combination  of  Efficiency  and  Smashing 
Point.  Price  of  the  Lamp  is  50  Cents  and  Cost  of  Electric 
Current  is  Assumed  at  10  Cents  per  Kilowatt  Hour 

Three  variables  are  considered  here.  The  two  independent  variables  are  repre- 
sented at  the  base  of  the  model  and  the  dependent  variable,  "cost",  is  read  from 
the  vertical  scale.  A  model  of  this  kind  can  be  made  from  plaster  of  Paris 
by  following  the  methods  described  in  detail  in  this  chapter 

known  in  which  portions  of  the  plaster  of  Paris  block  the  greatest 
amount  must  be  removed  before  the  wires  come  in  sight.  Knowledge 
of  the  position  of  the  wires  in  the  block  of  plaster  of  Paris  permits 
removing  the  plaster  rapidly  without  danger  of  taking  off  too  much. 
After  the  wires  do  come  into  sight,  the  ^nodel  must  be  carefully  scraped 
so  that  the  surfaces  will  have  uniform  curves  without  any  humps  or 


338  GRAPHIC    METHODS 

hollows.  If  all  the  surfaces  are  concave,  as  they  are  seen  to  be  in 
Fig.  237,  the  scraping  is  rather  a  simple  matter  since  the  surfaces 
between  the  two  wires  are  lower  than  the  wires  themselves.  If  a 
solid  model  were  made  for  data  such  as  that  of  Fig.  236,  much  care 
would  be  necessary,  for  in  that  case  some  of  the  surfaces  are  convex 
and  it  would  be  essential  that  enough  material  should  be  left  between 
the  different  wires  to  permit  giving  the  nicely  rounded  smooth  surfaces 
which  would  correctly  represent  the  data.  When  the  surfaces  have 
been  scraped  as  nearly  as  possible  to  the  proper  shape  they  may  be 
smoothed  by  rubbing  with  fine  sandpaper.  The  external  flat  faces 
of  the  model  may  also  be  sandpapered  advantageously  to  remove 
any  marks  which  may  remain  from  the  surface  of  the  box  used  as  a 
mold.  Lines  such  as  are  seen  in  Fig.  237  can  be  ruled  on  the  surface 
and  the  different  scales  can  be  lettered  by  hand.  A  few  coats  of  boiled 
linseed  oil  will  harden  the  surface  and  give  an  attractive  finish. 

In  Fig.  237  the  lines  giving  oval  figures  represent  certain  oper- 
ating conditions  which,  from  experiment  and  from  study  of  the  model 
itself,  have  been  found  to  be  most  desirable  in  practice.  The  oval 
lines  show  the  limiting  conditions  best  for  actual  practical  operation, 
and  give  the  real  conclusions  which  the  model  itself  greatly  assists 
in  portraying.  Solid  models  and  three-dimension  charts  like  those 
shown  are  of  supreme  value  in  studies  of  complex  data.  It  is  to  be 
regretted  that  these  methods  of  presentation  involve  so  much  labor 
that  they  cannot  be  used  as  frequently  as  might  be  desired. 

In  political  campaigns  frequent  use  is  made  of  statistical  informa- 
tion. Campaign  orators  use  figures  which  sound  impressive  when 
combined  with  a  certain  amount  of  eloquence.  Too  many  of  the  state- 
ments, however,  tell  only  a  portion  of  the  whole  truth,  and  that  por- 
tion is,  of  course,  assumed  to  be  the  portion  which  the  speaker  most 
desires  to  have  put  forward.  It  is  not  ordinarily  feasible  in  a  speech 
to  give  all  the  facts  over  a  series  of  years  so  that  the  hearer  may  draw 
any  conclusions  for  himself.  The  whole  system  is  weak  in  that  the 
audience  are  forced  to  depend  too  largely  on  the  statements  made 
by  the  orator,  rather  than  to  draw  conclusions  of  their  own  from  data 
which  are  warranted  to  be  authentic.  When  we  have  a  larger  number 
of  people  who  know  how  to  read  curves,  it  will  be  a  simple  matter 
to  present  the  arguments  of  a  political  campaign  by  means  of  a  pro- 
jecting lantern  with  properly  prepared  charts  thrown  on  a  screen. 
Even  now  the  charts  could  probably  be  so  made  as  to  be  understood 


GENERAL   METHODS  339 

and  correctly  interpreted  by  the  average  person  attending  a  political 
meeting,  with  resultant  increase  in  the  effectiveness  of  the  arguments 
they  support. 

In  municipal  campaigns,  especially,  the  lantern  talk  could  be  of 
very  great  interest  to  the  voters  if  the  slides  were  carefully  prepared 
and  arranged  in  a  logical  sequence.  By  using  simple  methods  of 
charting,  almost  any  kind  of  facts  could  be  portrayed  so  that  they 
would  surely  be  correctly  understood.  Concise  statements  in  con- 
junction with  the  charts  should,  of  course,  be  used,  somewhat  as  the 
main  titles  are  placed  under  the  illustrations  of  this  book.  Slides 
showing  snappy  questions  could  be  thrown  on  the  screen  rapidly, 
and  the  succeeding  slides  could  then  answer  the  questions.  Recent 
public  improvements,  bridges,  etc.,  could  be  illustrated  by  maps  and 
actual  photographs.  Pictures  of  fire  apparatus  and  views  showing 
the  efficiency  of  the  street-cleaning  methods,  etc.,  could  be  used  to 
add  interest  and  to  bring  out  certain  points  in  regard  to  the  operation 
of  specific  departments.  There  is  no  doubt  that  properly  prepared 
lantern  slides  would  have  great  weight  with  the  voters,  for  lantern 
slides  might  seem  to  present  a  less  biased  point  of  view  than  would 
the  average  partisan  campaign  orator. 

In  using  lantern  slides  for  campaign  purposes  it  is  not  necessary 
to  have  a  large  hall  for  each  showing  of  the  lantern  slides.  Auto- 
mobiles could  readily  be  equipped  so  that  two  cars  could  work  to- 
gether. One  auto  would  carry  a  screen,  which  could  be  very  quickly 
put  up,  somewhat  in  the  manner  of  a  sail,  when  that  part  of  the  town 
had  been  reached  where  the  lantern  talk  was  to  be  given  to  a  crowd 
in  the  street  or  on  some  vacant  lot.  The  other  automobile  could  carry 
the  lantern  on  a  stand  between  the  front  and  rear  seats.  The  power 
for  the  lantern  would  be  obtained  in  the  ordinary  manner  from  tanks 
of  oxygen  and  hydrogen  carried  in  the  car.  A  car  containing  the  lan- 
tern equipment  would  be  entirely  self-contained  and  no  electric  wires 
or  other  attachments  would  be  necessary.  The  lantern  car  would  be 
stopped  the  proper  distance  away  from  the  lantern  screen  on  the 
other  car,  and  the  slides  could  be  shown  on  the  screen  within  three 
minutes  after  arrival  in  any  desired  section  of  the  city.  In  thickly 
populated  districts  it  would  probably  not  be  necessary  to  announce 
a  political  meeting  of  this  kind,  as  word  would  be  passed  very  rapidly 
that  a  lantern  talk  was  in  progress  and  the  desired  crowd  would  collect 
spontaneously. 


340  GRAPHIC    METHODS 

One  very  great  advantage  of  the  lantern  presentation  in  political 
work  comes  from  the  fact  that  after  one  good  set  of  slides  has  been 
prepared,  these  slides  may  be  duplicated  at  very  small  expense.  Twen- 
ty or  even  fifty  sets  of  slides  might  be  shown  in  different  parts  of  a 
city  simultaneously  on  the  last  few  nights  just  before  election.  The 
main  candidates  are  never  able  to  make  speeches  at  all  of  the  desired 
points  during  the  last  few  days,  and  they  probably  always  feel  that  the 
last  days  or  hours  before  an  election  are  the  most  valuable  of  the  whole 
campaign.  When  many  sets  of  lantern  slides  are  made  from  the  same 
original  charts  there  is  very  little  additional  expense,  and  the  number 
of  people  who  may  get  the  benefit  of  the  carefully  prepared  slides  is 
tremendously  increased.  In  every  city  there  are  many  young  lawyers 
or  business  men  who  would  be  willing  to  make  a  speech  to  accompany 
the  slides  if  they  could  depend  upon  the  slides  for  their  main  material. 
The  number  of  people  who  may  be  reached  during  the  last  few  hours  of 
a  campaign  is  thus  almost  unlimited  if  the  lantern-slide  method  of  pres- 
entation is  used. 

From  the  educational  point  of  view,  it  would  probably  be  very  de- 
sirable to  have  lantern  slides  used  in  campaign  work,  because  there 
would  be  a  very  great  amount  of  valuable  information  conveyed  by 
the  slides  shown.  With  lantern  slides  showing  well  prepared  charts, 
probably  ten  times  as  much  information  could  be  absorbed  by  an  au- 
dience as  could  be  obtained  by  listening  to  the  most  expert  campaign 
speaker.  In  addition,  there  would  be  the  great  advantage  that  the 
facts  presented  by  lantern  slides  would  be  understood  and  remembered 
months  after  the  oratory  of  a  campaign  speaker  had  lost  its  beguiling 
effect  and  his  statements  been  forgotten. 

It  need  not  be  thought  that  lantern  talks  such  as  are  suggested  need 
be  devoid  of  all  those  spectacular  climaxes  which  are  so  common  with  a 
campaign  orator.  Whenever  it  is  desired  to  raise  some  enthusiasm,  a 
photograph  of  a  candidate  could  be  thrown  on  the  screen  and  a  cheer 
would  be  sure  to  follow.  There  is  an  almost  unlimited  field  for  the 
exercise  of  ingenuity  in  the  preparing  of  campaign  charts.  The  sets 
of  slides  would  have  tremendous  educational  value,  as  well  as  great 
power  in  presenting  political  arguments  in  such  manner  as  would  most 
positively  affect  the  vote. 

Methods  used  by  newspaper  offices  and  political  clubs  for  giving 
out  election  returns  to  great  crowds  in  the  streets  on  the  night  of  elec- 
tion day  are  not  all  that  they  might  be  made  if  a  little  thought  were 


I 


GENERAL   METHODS  341 

given  to  the  subject.  Though  the  projecting  lantern  is  now  used  almost 
universally  in  presenting  election  returns  in  large  cities,  thus  far  the 
lantern  slides  give  only  very  brief  scrawled  statements  that  certain 
cities  or  certain  districts  have  gone  for  some  particular  candidate 
with  some  estimated  plurality.  A  person  coming  out  into  the  street 
after  an  evening  at  the  theater  has  no  way  of  knowing  the  import  of 
the  various  telegraphic  statements  which  may  have  been  thrown  on 
the  screen  earlier  in  the  evening.  It  is  only  by  watching  the  bulletin- 
board  screen  for  half  an  hour  or  more  that  a  newcomer  is  able  to  get  any 
definite  idea  of  how  things  are  going. 

When  arrangements  have  already  been  made  for  using  a  lantern  to 
show  the  returns  on  a  screen,  it  would  cost  comparatively  little  more 
to  give  election  returns  which  would  be  of  much  interest  to  the  whole 
gathering,  as  well  as  of  great  effectiveness  in  showing  the  situation 
clearly  to  any  newcomer  who  might  join  the  crowd.  For  a  national 
election,  slides  could  be  prepared  to  the  number  of  twenty-five  or  more, 
giving  an  outline  map  of  the  United  States  and  showing  only  the  State 
lines.  As  the  returns  come  in,  some  man  well  acquainted  with  the 
political  situation  could  summarize  the  telegrams  received  up  to  the 
last  moment  and  give  his  opinion  as  to  which  candidates  are  leading 
each  State.  A  person  accustomed  to  coloring  lantern  slides  could  then 
immediately  color  in  one  of  the  map  slides  according  to  some  key,  so 
the  colors  red,  green,  yellow,  etc.,  on  different  areas  would  show  that 
certain  candidates  were  ahead  in  those  States  or  districts.  For  muni- 
cipal elections,  the  wards  and  different  divisions  of  the  city  could  be 
colored  in  exactly  the  same  manner  as  suggested  for  the  States.  The 
appearance  of  the  suggested  map  as  thrown  on  a  screen  may  be  judged 
somewhat  from  the  map  seen  in  Fig.  177.  It  would  add  much  to  the 
enthusiasm  of  the  crowd  if  it  were  announced  before  election  day  that 
some  well-known  person  would  make  the  summary  estimates  from  which 
the  colored  slides  would  be  prepared.  It  would  probably  take  less  than 
fifteen  minutes  to  color  a  lantern  slide  after  the  summary  had  been  made 
up  by  the  person  watching  the  telegrams,  and  it  would  be  feasible  to 
show  on  the  slide  itself  the  hour  at  which  the  slide  "went  to  press", 
as  9.30  p.m.,  9.45  p.m.,  etc.  As  a  new  slide  could  be  prepared  about 
every  fifteen  minutes,  a  map  summary  shown  on  the  screen  need  be 
only  about  fifteen  minutes  behind  the  latest  telegraphic  reports. 

In  addition  to  the  actual  colored  map,  each  slide  should  contain 
colored  bars  which  would  show  by  their  length  the  estimated  summary 


342  GRAPHIC   METHODS 

of  all  the  States  or  districts,  so  that  the  totals  of  different  candidates 
might  be  easily  compared.  Thus,  in  a  presidential  election,  the  count- 
ing of  the  number  of  States  for  each  candidate  does  not  by  any  means 
give  the  whole  story.  The  important  thing  is  the  number  of  electoral 
votes,  and  these  would  be  best  represented  by  the  bar  summary  which 
would  take  into  account  the  number  of  electoral  votes  of  each  State 
estimated  as  won  by  any  candidate.  With  the  combination  slide  show- 
ing, in  the  form  of  bars,  both  a  map  and  estimated  totals,  any  person 
coming  out  of  the  theater  to  join  the  election-night  crowd  could  see 
instantly  how  the  situation  stood  up  to  the  moment  the  last  slide  was 
colored. 

With  the  election-return  method  outlined,  the  concise  telegrams 
in  handwriting  would  still  be  shown  on  the  screen  one  by  one  as  the 
news  came  in  over  the  wire.  A  popular  appeal  to  a  large  crowd  can 
always  be  made  by  snappy  statements  such  as  "Jones  concedes  Chicago 
to  Smith",  or  "California  goes  for  Brown".  Instead  of  holding  state- 
ments of  this  kind  on  the  screen  until  other  news  could  arrive,  however, 
any  statement  in  written  words  would  be  taken  off  as  soon  as  it  had  been 
grasped  by  the  crowd  and  one  of  the  colored  maps  would  be  thrown  on 
the  screen.  Slides  with  colored  maps  and  colored  bars  would  be  used 
as  fillers,  to  be  kept  on  the  screen  continuously  whenever  there  were 
no  telegraphic  reports  to  be  projected  on  the  screen  in  written  words. 
It  would  probably  be  found  desirable,  in  many  cases,  to  show  telegraphic 
reports  in  such  manner  that  a  map  would  be  thrown  on  the  screen  be- 
tween each  two  telegraphic  reports,  and  also  held  on  the  screen  whenever 
telegraphic  reports  should  not  come  in  fast  enough. 

Election  returns  are  sometimes  told  to  a  whole  city  by  search  lights 
thrown  from  the  top  of  some  high  building.  National,  State,  or  munic- 
ipal election  returns  can  be  kept  distinct  by  the  search-light  method  if 
certain  directions,  north,  east,  south,  or  west  are  announced  for  the 
lantern  beams  referring  to  the  different  kinds  of  election  returns. 
Until  complete  reports  have  been  received  the  lantern  beams  can  be 
moved  gradually  up  and  down.  After  complete  reports  are  in  the  beam 
can  be  held  steady,  so  that  the  watchers  even  miles  away  may  know 
from  the  angle  of  the  light  and  its  position  that  a  conclusion  has  been 
reached,  and  who  wins. 

Educational  material  shown  in  parades  gives  an  effective  way  for 
reaching  vast  numbers  of  people.  Fig.  238  illustrates  some  of  the  floats 
used  in  presenting  statistical  information  in  the  municipal  parade  by 


GENERAL  METHODS 


343 


Photo  by  the  International  News  SerDice 

Fig.  238.    Statistical  Exhibits  in  the  Municipal  Parade  by  the  Employees  of  the  City 

of  New  York,  May  17,  1913 

Many  very  large  charts,  curves  and  other  statistical  displays  were  mounted  on  wagons  in  such  manner  that 
interpretation  was  possible  from  either  side  of  the  street.  The  Health  Department,  in  particular,  made 
excellent  use  of  graphic  methods,  showing  in  most  convincing  manner  how  the  death  rate  is  being  reduced 
by  modern  methods  of  sanitation  and  nursing 

the  employees  of  the  City  of  New  York,  May  17,  1913.  The  progress 
made  in  recent  years  by  practically  every  city  department  was  shown  by 
comparative  models,  charts,  or  large  printed  statements  which  could 
be  read  with  ease  from  either  side  of  the  street.  Even  though  the  day 
of  the  parade  was  rainy,  great  crowds  lined  the  sidewalks.  There  can 
be  no  doubt  that  many  of  the  thousands  who  saw  the  parade  came  away 
with  the  feeling  that  much  is  being  accomplished  to  improve  tlie  condi- 
tions of  municipal  management.  A  great  amount  of  work  was  neces- 
sary to  prepare  the  exhibits,  but  the  results  gave  ample  reward. 


Chapter  XVII 
A  FEW  CAUTIONS 

THE  title  for  any  chart  presenting  data  in  the  graphic  form  should 
be  so  clear  and  so  complete  that  the  chart  and  its  title  could 
be  removed  from  the  context  and  yet  give  all  the  information 
necessary  for  a  complete  interpretation  of  the  data.  Charts  which 
present  new  or  especially  interesting  facts  are  very  frequently  copied 
by  many  magazines.  A  chart  with  its  title  should  be  considered  a 
unit,  so  that  anyone  wishing  to  make  an  abstract  of  the  article  in 
which  the  chart  appears  could  safely  transfer  the  chart  and  its  title  for 
use  elsewhere.  In  the  preparation  of  this  book  it  has  been  found  that 
a  number  of  the  charts  used  have  been  copied  from  one  magazine  to 
another,  and  that  the  titles  under  the  charts  have  suffered  much  in  the 
copying.  This  is  due  chiefly  to  the  fact  that  the  titles  are  not  considered 
as  an  integral  part  of  a  chart,  and  that  many  magazine  editors  feel  at 
liberty  to  use  for  a  chart  whatever  title  they  happen  to  see  fit.  If 
each  chart  as  first  presented  has  a  complete  and  clear  title  it  will  greatly 
assist  in  establishing  a  practice  that  anyone  making  a  copy  of  a  chart 
should  copy  the  title  as  well  as  the  chart  itself. 

It  is  unfortunate  that  so  many  authors  send  in  illustrations  or  charts 
for  magazine  articles  without  the  titles  to  be  used  with  the  illustra- 
tions when  printed.  This  often  forces  the  editor  to  make  the  titles, 
and  if  he  does  not  have  complete  information  before  him  he  cannot  be 
blamed  if  he  makes  a  mistake  by  using  a  title  which  does  not  correctly 
represent*  the  data  of  the  chart.  To  avoid  the  possibility  of  error, 
the  editor  may  use  only  the  most  brief  title  under  the  illustration,  and 
then  trust  to  the  chart  being  fully  described  in  the  context  which  goes 
with  it.  In  such  a  case,  the  reader  who  may  happen  to  be  especially 
interested  in  the  chart  is  forced  to  plow  through  a  great  quantity  of 
context  to  find  the  particular  paragraph  which  may  happen  to  explain 
the  chart.     Though  it  is  true  that  great  care  is  necessary  to  give  in  a 

344 


A    FEW    CAUTIONS 


345 


wife  of 
£tner  of 

klnd  as 
uduated 
In  1884 

Ived  m 
he  late 


ay 
slighb.      ^a   saV 
s  he  cotitributed. 
r  Mrs.  Hayden,  no  o: 
re  just  where  she  was, 
roeder    sd,ld    that    some    wo 
fided  to  her  that  She  had  thou., 
ad   seen   Mrs.    Hayden  yesterday 
noon  In  New  Yot-t^. 


KANSAS  PROUD  OF  RECORD. 


Has    Reduced    Drinking    2,000    Per 
Cent.  In  30  Years — Jails  Are  Empty. 

Speciat  h  The  New  York  Times. 

TOPEKAv  Sept.  18.— That  Kansas  has 
reduced  Ita  drinking  2,000  per  cent.  In 
thirty  years,  and  Its  per  capita  consump- 
tion of  liquors  Is  how  $1.48  as  compared 
with  Missouri's  $24  a  year>  Is  the  tnes- 
eagre  sent  to  Tennessee  to-day  by  John 
S.  Dawson,  Attorney  General.  Tennessee 
ha*s  a  prohibition  fl^ht  oft  its  hands  this 
Fall. 

"The  test  of  value  of  prohibition 

1'     tv. 


Bureau 
day  defi 
as  Etrlc 
aim  up 
downw- 
dlrectlj 
Admij 
present 
nary 
agair 


D' 


few  words  a  title  for  a  complex  chart,  the  result  is  well  worth  the  effort 
and  a  chart  should  not  be  considered  complete  until  such  a  title  has 
been  made. 

When  large  numbers 
of  curves  and  charts  are 
used  by  a  corporation, 
it  will  be  found  advan- 
tageous to  have  certain 
standard  abbreviations 
and  symbols  on  the  face 
of  the  chart  so  that  in- 
formation may  be  given 
in  condensed  form  as  a 
signal  to  anyone  reading 
the  charts.  Fig.  240  is 
shown  here  as  an  ex- 
cellent example  of  what 
may  be  done  in  mak- 
ing symbols  which  would 
be  instantly  understood 
by  anyone  seeing  them. 
Though  these  particular 
symbols  are  not  fitted  for  use  in  chart  drawing,  they  may  give  a  sugges- 
tion of  the  possibilities  which  exist  for  abbreviating  into  symbol  form 
certain  remarks  or  instructions,  which  it  may  be  frequently  convenient 
to  place  on  the  face  of  a  chart  as  a  guide  to  prevent  misinterpretation 
by  the  reader.  If  the  symbols  for  chart  work  are  not  too  numerous, 
they  would  very  soon  be  understood  by  each  of  the  persons  who 
regularly  go  over  the  operating  charts  of  a  company. 

It  may  be  well  to  point  out  here  that  very  large  charts  are  sometimes 
a  disadvantage  rather  than  an  advantage.  In  preparing  reports, 
especially  those  reports  which  are  used  in  typewritten  form  for  limited 
distribution,  there  is  a  tendency  to  accompany  the  typewritten  report 
with  charts  on  very  large  sheets  of  paper,  bulky  and  inconvenient  to 
handle.  Sometimes  the  scales  of  these  accompanying  charts  are  so 
large  that  the  reader  is  puzzled  to  get  clearly  in  his  mind  what  the  whole 
chart  is  driving  at.  There  is  a  possibility  of  making  a  simple  chart  on 
such  a  large  scale  that  the  mere  size  of  the  chart  adds  to  its  complexity 
by  causing  the  reader  to  glance  from  one  side  of  the  chart  to  the  other 


Fig.  239.    A  Clear  and  Accurate  Title  is  of  Great 
Importance 

The  clipping  above,  taken  from  the  front  page  of  a  very  prom- 
inent newspaper,  shows  an  absurd  title.  If  a  thing  is  reduced 
100  per  cent,  it  is  all  gone.  How  can  drinking  be  reduced 
2,000  per  cent.'' 


346 


GRAPHIC    METHODS 


SHARP  TURN  TO  TME  RICNT 
J&  Si  iHl 


SHARP  TURN  TO  THE  UFT 
"&      ^      m 


STEEP  DESCENT 
^.  »  iS  «S 


STEEP  ASCENT 


\-/  n 


DEEP  HOLES  IN  XK  ROAD 

an  i"i  m 


TUNNEL 


SHARP  TURN  AND  ASCENT 
S;  (Hi  S  «  85 


SHARP  TURN  AND  DESCENT 


SERPENTINE 


BOAD  UNSUITABU  FOB  CARS 


RAILWAY  CROSSING  OANSEROUS  ROAD  CROSSINS 

Courtesy  of  "Motor" 

Fig.  240.    International  Road  Signs  that  Are  Being  Erected  on  the  Highways  of  Japan 

by  the  Nippon  Automobile  Club 

Any  conventional  symbols  or  signals  adopted  for  use  in  graphic  work  should  be  as  clear  and  suggestive  as  it 
is  possible  to  make  them.  The  above  illustration  is  shown  here  as  an  admirable  example  of  good  prac- 
tice in  the  making  of  graphic  symbols 

in  trying  to  get  a  condensed  visualization  of  the  chart.  There  are 
relatively  few  curve  charts  which  cannot  be  presented  for  report  pur- 
poses on  paper  8}^  by  11  inches,  the  commonest  size  used  for  a  type- 
writer. Though  the  placing  of  a  chart  on  paper  of  typewriter  size 
requires  more  care  than  is  necessary  if  a  very  large  sheet  of  paper  is  used, 
the  resulting  chart  is  frequently  more  easy  to  interpret  than  it  would 
be  if  made  to  a  larger  scale. 

A  warning  seems  justifiable  that  the  background  of  a  chart  should 
not  be  made  any  more  prominent  than  actually  necessary.  Many 
charts  have  such  heavy  co-ordinate  ruling  and  such  relatively  narrow 
lines  for  curves  or  other  data  that  the  real  facts  the  chart  is  intended  to 
portray  do  not  stand  out  clearly  from  the  background.  No  more  co- 
ordinate lines  should  be  used  than  are  absolutely  necessary  to  guide 
the  eye  of  the  reader  and  to  permit  an  easy  reading  of  the  curves.     Too 


A    FEW    CAUTIONS 


347 


many  magazine  articles  and  transactions  of  scientific  societies  contain 
charts  which  are  reproduced  direct  from  finely  ruled  co-ordinate  paper 
and  show  all  of  the  lines  of  the  co-ordinate  paper  in  the  finished  illus- 
tration. Co-ordinate  ruling  does  not  appear  prominently  on  most 
original  charts  because  the  ruling  is  usually  printed  in  some  color  of  ink 
distinct  from  the  curve  itself.  When,  however,  a  chart  is  reproduced 
in  a  line  engraving  the  co-ordinate  lines  come  out  the  same  color  as  the 
curve  or  other  important  data,  and  there  may  be  too  little  contrast  to 
assist  the  reader. 

Curves  are  sometimes  shown  plotted  vertically  when  a  horizontal 
arrangement  could  be  used  without  any  difficulty.    There  seems  to  be  no 


1910 
1911 

.  Cylinder  Bore         «/        ^         ^ 

/0/5         sol''        zofo         '^o/o         soT<>         boyo        70/'        ao7'         90% 

1 

ul 

.i 

n 

1912 

1 

i 

i 

1 

1913 

/] 

\  ^ 

^ 

^ 

'y 

N 

^ 

^ 

/o%       so%      30%       ^0%       i>-o^      00%        7070      ao%        9oya 


i9<o 


1911 


I9«2 


1913 

•910 
1911 
I9»2 
1913 

Courtesy  of  "Motor" 

Fig.  241.    Comparison  of  American  Automobiles  for  Four  Years,  in  Cylinder  Bore, 
Valve  Arrangement,  and  Ignition  System 

There  is  no  necessity  for  plotting  curves  in  the  vertical  position  shown  here  for  it  is  only  confusing  to  the 
reader.  These  curves  cannot  be  read  conveniently  even  by  turning  the  book  to  read  from  the  left 
because  some  of  the  type  would  then  be  upside  down.     See  Fig.  242 


Ignition  SyptenTp      ^        ^        ^ 

/o%       ao%       30%'      4ofo       so%       6o%        70/0       aojo        90^0 

1 

r/ 

1 

f 

^ 

k 

L% 

f 

1 

^ 

V 

s 

\ 

Z 

^ 

L 

348 


GRAPHIC    METHODS 


real  reason  why  Fig.  241  should  have  the  curves  arranged  in  the  ver- 
tical direction.  The  vertical  arrangement  confuses  the  reader  until 
he  ascertains  how  the  curves  may  be  read  by  turning  the  book  so  that 
the  curves  may  be  read  from  the  left  in  their  proper  position. 

Fig.  242  shows  the  data  of  Fig.  241  plotted  in  standard  manner 
Fig.  242  is  also  of  interest  because  it  shows  curves  plotted  from  only 
a  few  points  for  each  curve.     Though  one  may  be  tempted  to  use 
some  other  method  than  curve  presentation  when  only  few  points 


Percent 
lOO 


90 


80 


*70 


eo 


50 


40 


30 


20 


to 


O 


/ 

/ 

^ 

to  A.49 

/ 

< 

<s 

^os' 

V 

\ 

\ 

9  ' 

"*o  3S 

L*" 

^     s- 

to  5-49 

^ 

-iinder 

^ 

*«^\ 

5.5  *- 

r 1 

Percent 

lOO 


SO 


SO 


70 


60 


50 


AO 


30 


20 


10 


RerCent 

100 


1910    n 


12 


13        \Q\0 


90 


80 


70 


60 


50 


-40 


30 


20 


10 


..0.^/ 

li^e^ 

^ 

/ 

/ 

^<^o. 

« 

^^<j 

\ 

N 

^^^ 

•^fiv 

.^ 

% 

1^ 

SB 

1910     'II       *I2       '13 


Cylinder  Valve  Ignition 

Bore  Arrangement  Systems 

Fig.  242.     Comparison  of  American  Automobiles  for  Four  Years,  in  Cylinder  Bore, 
Valve  Arrangement,  and  Ignition  System 

The  standard  arrangement  of  the  curves  on  this  chart  permits  easy  reading.     Notice  that  curves  are  per- 
fectly feasible  as  a  method  of  presentation  even  though  there  are  only  a  few  points  available  for  each  curve 


A    FEW   CAUTIONS 


349 


for  a  curve  are  available,  it  can  be  seen  that  even  if  there  were  only 
three  points  instead  of  four  in  Fig.  242,  the  curve  would  still  be  valu- 
able to  convey  the  desired  information.  In  Fig.  53  and  Fig.  54  methods 
are  shown  by  which  charts  which  are  essentially  curve  charts  may  be 
drawn  even  though  there  are  available  only  two  points  for  each  curve. 


Shoriage 


Surplus 


Shorfage    1908 


Surplus 


Jan    Z 
Feb.   f> 


Box  Cam 


/III  Can,.. 


Oct.  14 

^-      IB 
Nov.  1 1 


100,000 


00,000        ZOO.OO0 


300.O0O      4«)J000 


Shor-fage 


^Surplus 


Bojr  Cars 


All  Cars 


Shorfage 


Surplus 


lOO.OOC       ZOO.OOO 


American  RaUway  Assodatlon 

Fig.  243.    Freight-Car  Shortage  and  Surplus  in  the  United  States  for  Four  Years, 

1907  to  191 1,  Inclusive 

The  horizontal  bars  here  are  so  numerous  and  are  placed  so  close  together  that  the  charts  have  practically 
the  general  form  of  curves  drawTi  vertically  instead  of  horizontally.  It  would  seem  just  as  well  to  repre- 
sent the  data  by  real  curves  drawn  with  the  standard  horizontal  arrangement 

When  curves  become  as  widely  understood  as  the  bar  method  of 
presentation,  it  will  be  found  that  curves  can  be  used  advantageously 
in  almost  every  case  where  it  is  now  common  to  use  either  vertical 
or  horizontal  bars. 

In  Fig.  243  the  horizontal-bar  method  has  been  elaborated  so  that 
the  resulting  chart  has  practically  the  general  effect  which  would 
be  obtained  by  a  curve  chart.  The  reader  who  wishes  to  read  Fig. 
243  in  the  form  of  curves  is,  however,  forced  to  turn  the  book  so  that 
he  may  see  the  chart  from  the  left  with  the  curves  running  in  a  generally 
horizontal  direction.  The  data  would  likely  be  just  as  well  understood 
by  railroad  men  if  shown  by  real  curves  drawn  in  the  standard  manner. 


350 


GRAPHIC   METHODS 


.^■ 

18 
1896 

9718 
1898 

99  19 
1900 

01  19 
1902 

0319 
1904 

0519 
1906 

91 19 
1908 

09  1911 

pio\ 

46 

JJ 

,--^ 

49 

Afl 

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/ 

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32 

/ 

' 

30 

f^ 

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28- 

^ 

^^ 

/. 





26- 

— 

— 

— 

— 

ZI 

— 

New  York  Times  Annalist 

Fig.  244.  Average  per  Capita  in  the 
United  States  of  Total  Savings-bank 
Deposits 

At  first  glance  the  impression  is  that  Americans  are 
growing  rich  very  rapidly.  Yet  total  deposits 
per  capita  have  not  doubled  in  the  sixteen  years 
shown.  If  the  bottom  line  of  the  chart  were  at 
the  zero  of  the  vertical  scale,  an  entirely  different 
impression  would  be  given.     See  Fig.  245 


At  numerous  places  through- 
out this  book  criticisms  have 
been  made  of  curves  and  charts 
in  which  no  zero  hne  for  the 
vertical  scale  was  shown  on  the 
chart.  Though  this  subject  has 
been  mentioned  elsewhere  it  seems 
best  to  show  here  a  few  examples 
on  the  same  general  argument. 
In  Fig.  244  the  first  glance  im- 
pression that  savings-banks  de- 
posits have  increased  with  great 
rapidity  is  not  entirely  confirmed 
when  it  is  noticed  that  the  left- 
hand  scale  does  not  begin  anywhere 
near    zero.     It    is    nearly    always 


possible  to  make  a  chart  so  that 
the  zero  of  the  vertical  scale  will  show.  Usually,  of  course,  the  zero 
line  is  at  the  bottom  of  the  chart  unless  there  are  negative  quantities 
so  that  the  curve  crosses  over  the  zero  line  and  extends  below  it. 
In  all  cases  the  zero  line  can  be  made  a  heavy  line.  If  the  curve  should 
extend  below  the  zero  line  the  width  of  the  zero  line  should  be  so 
great  that  the  reader  will  be  cer- 
tain to  interpret  the  chart  from 
the  zero  line  rather  than  from 
the  bottom  line  of  the  chart  it- 
self. 

It  sometimes  happens  that  the 
data  for  a  chart  involve  high  numeri- 
cal figures  so  that  a  large  amount 
of  space  must  be  used  if  the  zero 
line  of  the  vertical  scale  is  to  be 
shown  in  the  final  illustration.  In 
such  a  case,  the  bottom  of  the  chart 
may  have  a  wavy  line  as  seen  in 
Fig.  245  which  portrays  the  same 
data  as  Fig.  244,  Fig.  244  could 
have  been  extended  so  that  the  bot- 
tom line  would  be  the  zero  line  if  a 


$ 

78 
J896 

9718 

1898 

9.9  19 
1900 

01  19 
1902 

0319 
1904 

0519 
1906 

91 19 

J908 

09  19 
1910 

77 

4(i 

JJ 

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J 

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r 

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4 

— 

— 

— 

— 

— 

— 

— 

E 

^ 

B 

;:= 

:z. 

^ 

"Z- 

~ 

^ 

— 

~ 

Fig.  245.  Average  per  Capita  of  Total 
Savings-bank  Deposits  in  the  United 
States 

Whenever  possible  a  chart  containing  curves  should 
be  so  drawn  that  the  zero  of  the  vertical  scale 
appears  in  the  chart.  If  the  zero  line  is  not 
shown  on  the  chart,  that  fact  should  be  indicated 
by  a  wa\'y  line  at  the  bottom  warning  the  reader 
that  interpretation  must  be  made  from  the  ver- 
tical scale  and  not  by  visual  measurement  from 
the  bottom  line  of  the  chart 


A    FEW    CAUTIONS 


351 


Elmer  Ritlenhouse.  in  the  New  York  Times 

Fig.  246.  Comparison  of  Death  Rates  in  the  United  States,  Showing  Reduction  in 
Death  Rate  for  Tuberculosis  and  Increase  in  Death  Rate  for  Degenerative  Dis- 
eases 

The  chart  gives  the  impression  of  very  rapid  decreases  and  increases,  chiefly  because  the  bottom  line  is 
not  at  the  zero  of  the  vertical  scale.  The  figures  used  for  the  vertical  scale  are  rather  small  in  size  and 
the  rapid  reader  is  not  likely  to  notice  that  the  scale  does  not  begin  at  zero.  Compare  Fig.  247  and  Fig. 
248 


somewhat  greater  amount  of  photographic  reduction  had  been  used 
in  making  the  hue  engraving  or  if  the  proportions  between  the  hori- 
zontal- and  vertical-scale  distances  had  been  changed  somewhat. 
There  is  really  no  necessity  for  using  the  wavy  line  for  the  bottom 
of  Fig.  245  since  the  chart  would  have  been  better  made  with  the 
zero  line  showing  the  bottom.  Fig.  245  will  serve,  however,  as  an 
example  to  illustrate  how  the  wavy  line  can  be  drawn  to  any  chart 
where  it  is  really  inconvenient  to  extend  the  chart  itself  so  that  the 
zero  line  may  show. 

Dea-bh  Rate 
Per  10.000 


36 
3a 
28 
ZA- 
20 
16 
^2 
8 


teao 


1©90 

•Tuberculosis 


1900 


010 


m^mm  Degenera-Liv6    Diseases 
(Heart,  Kidney,  etc.) 

Data  of  Elmer  Riltcnhouse 

Fig.  247.  Comparison  of  Death  Rates  in  the  United  States,  Showing  Reduction  in 
Death  Rate  for  Tuberculosis  and  Increase  in  Death  Rate  for  Degenerative  Dis- 
eases 

This  chart  is  made  from  the  same  data  as  Fig.  246.     Here  the  zero  line  is  shown  and  the  changes  in  death 
rate  appear  much  less  rapid  than  they  do  in  Fig.  246.     See  also  Fig.  248 


352 


GRAPHIC    METHODS 


Fig.  246  gives  another  example  where  neglecting  to  show  the  zero 
line  may  cause  an  entirely  erroneous  impression  regarding  the  facts 
which  the  chart  is  intended  to  bring  out.  The  failure  to  show  the 
zero  line  at  the  bottom  of  a  chart  is  so  common  a  fault,  found  in  nearly 
all  publications,  that  some  typical  examples  are  shown  here  in  the 
hope  that  a  bad  practice  may  be  somewhat  reduced. 

Fig.  247  gives  the  data  of  Fig.  246  redrawn  so  that  the  zero  line 
is  shown  at  the  bottom  of  the  chart.  It  is  believed  that  this  illustra- 
tion will  prove  conclusively  how  great  an  error  may  be  made  if  charts 
are  read  hastily  on  the  assumption  that  the  bottom  line  of  the  chart 
is  the  zero  line.  Since  some  persons  are  almost  sure  to  read  a  chart 
from  the  bottom  line,  it  seems  desirable  that  all  charts  should  be  so 
made  that  the  reader  may  interpret  from  the  bottom  line  as  a  zero 
line,  or  else  receive  positive  warning  that  he  should  not  do  so. 


Data  of  Elmer  tvuuntwusc 


Fig.  248.  Comparison  of  Death  Rates  in  the  United  States,  Showing  Reduction  in 
Death  Rate  for  Tuberculosis  and  Increase  in  Death  Rate  for  Degenerative  Dis- 
eases 

This  illustration  is  identical  with  Fig.  246  except  that  here  a  wa\'y  line  is  used  at  the  base  showing  that  the 
bottom  of  the  chart  is  not  at  the  zero  of  the  vertical  scale.  It  is  always  desirable  to  have  the  bottom  line 
at  zero.     If  that  is  not  possible  the  wavy  line  should  be  used  as  a  warning  to  the  reader 

Though  there  is  no  necessity  for  showing  Fig.  246  without  having 
a  zero  line  at  the  bottom  of  the  chart.  Fig.  248  is  presented  here  to 
prove  how  easy  it  is  to  make  a  wavy  line  at  the  bottom  of  a  chart  if 
there  should  be  any  real  reason  why  the  chart  cannot  be  made  so 
as  to  include  the  zero  line  of  the  vertical  scale.  Fig.  248  is  exactly 
the  same  as  Fig.  246  except  that  the  wavy  line  is  used  instead  of  the 
straight  line  at  the  bottom. 

The  beginner  in  curve  plotting  and  in  curve  reading  is  apt  to  be 
somewhat  puzzled  by  the  different  effects  which  may  be  obtained  by 
changing  the  ratio  between  the  vertical  scale  and  the  horizontal  scale. 
It  is  difficult  to  give  any  general  rules  which  would  assist  in  overcoming 
the  beginner's  confusion.  Ordinarily  the  best  way  to  get  facility 
in  making  the  proper  choice  of  vertical  and  horizontal  scales  for  plot- 


A    FEW    CAUTIONS  353 

ting  curves  is  to  take  one  set  of  data  and  plot  those  data  in  several 
different  ways,  noticing  the  changes  which  the  different  scales  selected 
give  in  the  proportions  of  the  chart.  Just  as  the  written  or  spoken 
English  language  may  be  used  to  make  gross  exaggerations,  so  charts 
and  especially  curves  may  convey  exaggerations  unless  the  person 
preparing  the  charts  uses  as  much  care  as  he  would  ordinarily  use  to 
avoid  exaggeration  if  presenting  his  material  by  written  or  spoken 
words.  Most  authors  would  greatly  resent  it  if  they  were  told  that 
their  writings  contained  great  exaggerations,  yet  many  of  these  same 
authors  permit  their  work  to  be  illustrated  with  charts  which  are 
so  arranged  as  to  cause  an  erroneous  interpretation.  If  authors  and 
editors  will  inspect  their  charts  as  carefully  as  they  revise  their  written 
matter,  we  shall  have,  in  a  very  short  time,  a  standard  of  reliability 
in  charts  and  illustrations  just  as  high  as  now  found  in  the  average 
printed  page. 

Fig.  249  shows  an  interesting  application  of  the  use  of  charts  to 
corporation  reports.  The  back  page  of  the  annual  report  of  the  Ameri- 
can Telephone  and  Telegraph  Company  has  the  proportions  seen  in 
Fig.  249.  As  a  report  to  stockholders  is  intended  to  be  as  optimistic 
as  possible  within  the  limits  of  truthfulness,  there  can  scarcely  be  any 
criticism  that  the  chart  was  so  made  that  the  growth  in  business  was 
shown  on  the  long  direction  of  the  page  instead  of  on  the  short  dimen- 
sion of  the  page.  The  chart  in  Fig.  249  is  simple  to  understand,  and 
probably  very  few  stockholders  would  have  any  difficulty  in  making  a 
fairly  accurate  interpretation.  For  the  annual  report  of  a  corporation, 
it  is  likel}''  that  the  vertical-bar  method  of  Fig.  249  is  preferable,  from 
an  advertising  standpoint,  to  a  smooth  curve  like  that  shown  in  Fig.  250. 

One  special  point  relating  to  Fig.  249  is  worthy  of  mention.  At  the 
bottom  of  the  chart  will  be  noticed  the  statement  that  the  figures  re- 
corded are  those  of  "January  1st  of  each  year".  This  statement  may 
lead  to  an  erroneous  conclusion  on  the  part  of  the  reader,  for  he  may 
feel  that  the  difference  in  height  between  the  bar  marked  1911  and  that 
for  1912  shows  the  number  of  telephones  installed  during  1912,  when, 
in  reality,  it  shows  the  number  of  telephones  installed  during  1911, 
since  the  bars  represent  the  number  of  'phones  installed  to  the  first  of 
January  of  each  year.  If  the  statement  at  the  bottom  of  the  chart  had 
been  made  "December  31st  of  each  year"  there  would  be  no  danger 
of  misinterpretation.  If  the  statement  were  made  for  December  31 
it  would,  of  course,  be  necessary  to  change  the  numbers  at  the  bottom 


DIAGRAM 

SHOWING  THE  GROWTH  IN 

SUBSCRIBERS'  STAllONS 

CONNECTED  TO  THE  SYSTEM 
OF  THE 

BELL  TELEPHONE 
COMPANIES 

FROM 

JAN.  1,1878— JAN.  1,1912. 


On  January  I,   1912,  thers  was  one  Bell  Telephone 

Station  to  each  14  of  the  Total   Population  of  the 

United  States. 


t± 


.700.000 
600.000 
500.000 
400,000 
300.000 
200.000 
100,000 
000,000 
900,000 
800.000 
700.000 
600.0C0 


1876  18?8  1880  1882  1884  1886  1888  1890  1832  im  1896  J898  1900  1%^^ 
JANUARY  1st  OF  EACH  YEAR. 


5,600,000 
5,400.000 
5.300.000 
5.200.000 
5,100,000 
5,000,000 
4,900.000 
4,800.000 
4,700.000 
4,600,000 
4,500.000 
4,400.000 
4.300.000 
4,200,000 
4,100,000  to 
4,000,000g 
3.900.000f: 
3.800.000  < 
3,700.000  « 
3.600.000. 
3,500.000^ 
3,400.000  UJ 
3,300.0005 
3,200,0000 
3,100.000g 
3,000,0003 
2,900,000'* 
2,800.000}!; 
2,700.000 
2,600,000  £ 
2,500.000  m 
2.400,000^ 
2,300.0002 
2,200.000 
2,100.000 
2,000.000 
1.900.000 
1.800.000 
1,700.000 
1,600.000 
1,500.000 
1,400,000 
1,300.000 
1.200.000 
1i  100,000 
1,000,000 
900,000 
800.000 
700,000 
600,000 
500,000 
400,000 
300,000 
200,000 
100,000 
0 


American  Telephone  &  Telegraph  Co. 

Fig.  249.    The  Number  of  Subscribers'  Stations  Connected  to  the  System  of  the  Bell 

Telephone  Companies 

This  illustration  was  shown  on  the  back  cover  of  the  1911  annual  report  to  stockholders  of  the  American 
Telephone  &  Telegraph  Company.  For  the  average  stockholder  the  vertical  bars  would  probably  be 
understood  more  readily  than  the  curve  shown  in  Fig.  250.     Compare  with  Fig.  250  and  Fig.  251 

354 


6,700,000 
6,600,000 
6,500,000 
6,400,000 
6,300,000 
6,200,000 
6,100,000 
6,000,000 
6,900,000 
6,800,000 
5,700,000 
5,600,000 
5,500,000 
5,400,000 
6,300,000 
5,200,000 
6,100,000 
5,000,000 
4,900,000 
4,800,000 
4,700,000 
4,600,000 
4,600,000 
4,400,000 
4,300,000 
4,200,000 
4,100,000 
4,000,000 
3,900,000 
3,800,000 
3,700,000 
3,600,000 
3,500,000 
3,400,000 
3,300,000 
3,200,000 
3,100,000 
3,000,000 
2,900,00C 
2,800,000 
2,700,000 
2,600,000 
2,500,000 
2,400,000 
2,300,000 
2,200,000 
2,100,000 
2,000,000 
1,900,000 
1,800,000 
1,700,000 
1,600,000 
1,600,000 
1,400,000 
1,300,000 
1,200,000 
1,100,000 
1,000,000 
900,000 
800,000 
700,000 
600,000 
600,000 
400,000 
300,000 
200,000 
100,000 
0 


13 

J 

J 

J 

T 

f_ 

niAABAM                                                                                  L 

SHOWING  THE  GROWTH  IN                                                        / 

J 

SUBSCRIBERS'  STATIONS                             J 

CONNECTED  TO  THE  SYSTEM                                                                 T 

OF  THE                                                                                    r 

REIJ,  TELEPHONE                 T 

rniwPAiviFQ                   1 

\AJairAi^lKji3                                  J 

FROM                                                                                  T 

nlAlV   1    1fi7fi      TATVr  1    t01'>                                        1 

d/iii*  1}  Xo/D     J  All  •  1,  XtlL^*                                  r 

1 

On  Januaiy  1,  1912,  thera  wat  ons  Bell  Telephone                                                 1 

T 

/ 

F 

1 

J 

J 

7 

T 

1] 

1 

J 

7 

f 

r 

1 

1 

7 

T 

r 

1 

T 

T 

r_ 

i 

/ 

f 

/ 

/ 

/ 

j 

f 

a 

/ 

i^ 

/ 

^        1 

^^ 

tl                                             **^  ^"^^ 

io«t"000>OTHe«M^io«ot-ooo>OTH<seo'*iou3t»oooiO'-i«eoTiiiotoc-e050'-; 
i<*h«b.h.t.QOcocoooeocoajoQcOQaAAAa)a)a)na>a)AOOooooooOO^*^ 


6,700,000 
6,600,000 
6,500,000 
6,400,000 
6,300,000 
6,200,000 
6,100,000 
6,000,000 
5,900,000 
5,800,000 
5,700,000 
6,600,000 
5,500,000 
5,400,000 
5,300,000 
5,200,000 
5,100,000 
5,000,000 
4,900,000 
4,800,000 
4,700,000 
4,600,000 
4,500,000 
4,400,000 
4,300,000 
4,200,000 
4,100,000 
4,000,000 
3,900,000 
3,800,000 
3,700,000 
3,600,000 
3,500,000 
3,400,000 
3,300,000 
3,200,000 
3,100,000 
3,000,000 
2,900,000 
2,800,000 
2,700,000 
2,600,000 
2,500,000 
2,400,000 
2,300,000 
2,200,000 
2,100,000 
2,000,000 
1,900,000 
1,800,000 
1,700,000 
1,600,000 
1,500,000 
1,400,000 
1,300,000 
1,200,OCO 
1,100,000 
1,000,000 
900,000 
800,000 
700  000 
600,000 
500,000 
400,000 
300,000 
200,000 
100,000 
0 


Fig.  250.    The  Number  of  Subscribers'  Stations  Connected  to  the  System  of  the  Bell 
Telephone  Companies,  December  31st  of  Each  Year 

The  curve  permits  quicker  and  more  accurate  interpretation  than  the  vertical  bars  but  unfortunately  curves 
are  not  readily  understood  by  as  many  people.  Note  that  the  date  on  which  the  telephones  are  recorded 
is  here  specified  as  December  31st  instead  of  as  January  1st.     Compare  Fig.  251 

355 


356 


GEAPHIC    METHODS 


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A    FEW    CAUTIONS  357 

of  each  vertical  bar  so  that  they  would  appear  in  each  case  one  less  than 
the  figures  given.  With  Fig.  249  as  it  is,  the  1908  bar  shows  a  great 
increase  over  1907  and  the  reader  is  quite  justified  in  wondering  how 
it  happened  that  a  greatly  increased  number  of  telephones  were  installed 
during  a  panic  year.  From  the  chart  as  shown  the  reader  is  not  likely 
to  realize  that  1908  is  getting  credit  for  the  telephones  installed  during 
1907,  which  happened  to  be  a  very  prosperous  business  year.  Having 
the  data  recorded  as  of  December  31  each  year  overcomes  the  difficulty 
and  makes  certain  that  no  false  impression  can  be  obtained. 

Fig.  250  shows  the  data  of  Fig.  249  plotted  as  a  smooth  curve.  For 
a  trained  class  of  readers  the  curve  presentation  is  preferable  to  the  bar 
presentation,  for  it  permits  seeing  the  fluctuations  which  have  occurred 
from  year  to  year  more  easily  than  they  can  be  seen  by  glancing  from 
bar  to  bar  in  Fig.  249.  Within  a  few  years  it  is  probable  that  curves 
will  be  so  well  understood  that  a  report  to  stockholders  could  best  be 
made  using  the  method  of  Fig.  250  instead  of  the  method  of  Fig.  249. 

In  order  to  show  the  different  impressions  which  may  be  had  if 
various  proportions  between  the  horizontal  and  vertical  scales  are  used. 
Fig.  251  has  been  plotted  from  the  same  data  as  Fig.  249  and  Fig.  250. 
For  Fig.  251  an  assumption  was  made  that  the  chart  would  be  printed 
on  exactly  the  same  size  page  as  was  used  for  Fig.  249.     The  scales  for 
Fig.  250  were,  however,  arranged  in  the  other  direction  on  the  page  and 
the  co-ordinate  ruling  was  made  so  that  some  space  would  be  allowed 
for  extension  of  the  curve  in  future  years.     As  seen  from  Fig.  251  the 
growth  in  the  telephone  business  does  not  appear  nearly  so  rapid  as 
would  be  thought  from  observing  Fig.  250.     Each  of  these  charts  is, 
however,  plotted  to  exact  scale  and  the  difference  in  the  impression 
obtained  is  caused  only  by  the  proportions  of  the  vertical  and  the  hori- 
zontal scales.     The  appearance  of  less  rapid  growth  in  Fig.  250  is 
assisted  somewhat  by  the  fact  that  the  large-type  title  of  the  chart  is 
arranged  horizontally  instead  of  in  the  form  of  a  square  as  seen  in  Fig. 
250.     The  heavy  black  type  with  much  greater  spread  horizontally 
than  vertically  tends  to  overshadow  the  curve  itself  and  causes  for  the 
curve  a  more  distinctly  horizontal  impression  than  would  otherwise 
be  obtained.     A  person  reading  charts  must  take  great  care  that  he 
does  not  give  too  much  weight  to  the  actual  appearance  of  the  curve 
on  the  page,  instead  of  basing  his  conclusions  on  the  percentage  increase 
or  decrease  as  judged  from  the  figures  of  the  vertical  scale.     The  proper 
choice  of  scales  for  curve  plotting  is  largely  a  matter  of  judgment,  and 


358 


GRAPHIC    METHODS 


Courtesy  of  the  Grolier  Society 

Fig.  252.    An  Optical  Illu- 
sion 

The  black  line  at  the  left  appears 
longer  than  the  one  at  the  right. 
The  two  lines  are,  however,  of 
the  same  length 


the  judgment  can  be  trained  very  greatly  if  it  is  kept  in  mind  to  examine 
every  curve  chart  which  comes  to  one's  attention  to  see  whether  the 
vertical  and  horizontal  scales  have  been  so  selected  that  the  chart  gives 
\        ..•*  a  fair  representation  of  the  facts. 

The  English  language  has  so  many 
words  with  double  meaning  and  so  many 
words  for  which  the  shades  of  meaning 
are  rather  indistinct  that  there  are  really 
many  more  chances  of  false  impression 
from  the  written  or  spoken  language  than 
there  are  from  the  data  expressed  in  graphic 
form.  Nevertheless,  a  few  examples  of  op- 
tical illusions  are  shown  here  so  that  the 
reader  may  have  some  idea  of  those  peculiar 
things  which  may  enter  in  to  cause  strange  impressions  if  charts  do  not 
receive  some  degree  of  preliminary  care  and  final  inspection.  Though 
many  of  the  effects  seen  in  Fig.  252,  Fig.  253,  Fig.  254,  Fig.  255,  and 
Fig.  256  are  not  likely  to  appear  in 
ordinary  chart  work,  they  may  not- 
withstanding cause  difficulty  in  some 
kinds  of  very  large  wall  exhibits.  Fig. 
254,  in  particular,  shows  an  efl^ect  which 
is  to  be  avoided  where  large  quan- 
tities of  black  ink  are  used.  In  a 
recent  series  of  charts  comparisons  were 
made  between  different  white  squares, 
surrounded  in  each  case  by  a  black 
border  practically  as  wide  as  the  square  at  the  center.  It  is  not  likely 
that  a  reader  seeing  a  series  of  black  squares  with  white  centers  of  dif- 
ferent size  would  be  able  to  judge  correctly  the  relative  size  of  the 

white  squares  at  the  center. 

Fig.    256    shows    some    of    the   difficulties 
which    may    be    encountered    if    an    attempt 
is    made    to   present  data  by  comparing  the 
relative  heights  of  pictures  of  the  human  form. 
Courtesy  of  the  GToiier  sociciy     Thcrc   arc   fcw  pcoplc  wlio  will  bclievc  until 

Fig.  254.    An  Optical  Illu-  ^^        ^^^^^    measurements     that    the    figure 

sion 
The  white  square  appears  larger  of    the    girl    in  Fig.   256   is   really   of  greater 

ai-Hf^the  slme^Sze^^^  ^  ^  ^^^  length  than  that  of  the  policeman.   The  illusion 


Courtesy  of  the  Grolier  Society 

Fig-  253.    An  Optical  Illusion 

The  left-hand  arrangement  looks  wider  than 
it  is  high  while  the  right-hand  arrange- 
ment looks  higher  than  it  is  wide.  On 
each  side  the  height  is  the  same  as  the 
width 


A    FEW    CAUTIONS 


359 


is  caused  chiefly  by  the  perspective  hues  of  the  drawing  which  force 

one  to  estimate  relative  height  to  a  certain  extent  by  the  number  of 

perspective  lines  intersected  instead  of  by  the  actual  size  of  the  black 

pictures. 

Before   charts    are   sent   to   an  engraver  to 

have   plates   made    for    printing    it    is   wise   to 

have  each  chart  run  the  gauntlet  of  a  series  of 

questions,  so  that  the  time  of  the  person  doing 

the  checking  may  be  saved   and   also   that   the 

points     more     frequently    overlooked    may    be 

thoroughly  considered  in  each  case.     Below  are 

given  a  series  of  questions  which  may  be  found 

convenient  to  anyone  having  charts  to  prepare. 

This   list   is   not  by  any  means  complete,  and 

the  questions  are  given  here  as  general  sugges- 
tions only.     The  person  checking  a  chart  simply 

reads  the  ques- 
tions one  by  one 
from  the  book, 
and  then  care- 
fully observes 
the  chart  to  see 
whether  it  comes 
up  to  the  stand- 
ard. Whenever 
possible  it  is  well 
to  have  the  chart  Illusion 

checked  by  some  ^te  columns  appear  bent  The 
•^  left-hand  pair  seem  closest 

person  other  than  at  the  ends,  while  the  right- 
hand  pair  seem  closest  at 
the  center.  The  sides  of  the 
columns  are  really  straight 
and  parallel 


the  one  who  drew 
it.  In  every  edi- 
torial   office    the 

fact  is  recognized  that  one  proof-reader 
will  find  important  errors  that  were 
overlooked  by  another  reader  equally 
expert.  Further,  a  mind  much  occupied 
with  an  idea  may  often  fail  to  see  important  gaps  in  its  statement, 
verbal  or  graphic,  until  perhaps  they  are  noted  by  someone  less  familiar 
with  the  subject.    Two  points  of  view  are  always  better  than  one. 


CouTUsy  of  the  Orolicr  Society  and  of  Popular  Mechanics 

Fig.  256.    An  Optical  Illusion 

The  policeman  appears  much  taller  than  the 
girl.  In  reality  the  figure  of  the  girl  is  y^ 
inch  taller  than  the  figure  of  the  policeman 


360  GRAPHIC    METHODS 

CHECKING  LIST  FOR  GRAPHIC  PRESENTATIONS 

1.  Are  the  data  of  the  chart  correct? 

2.  Has  the  best  method  been  used  for  showing  the  data? 

3.  Are  the  proportions  of  the  chart  the  best  possible  to  show  the 
data? 

4.  When  the  chart  is  reduced  in  size  will  the  proportions  be  those 
best  suited  to  the  space  in  which  it  must  be  printed? 

5.  Are  the  proportions  such  that  there  will  be  sufficient  space  for 
the  title  of  the  chart  when- the  chart  has  been  reduced  to  final  printing 
size? 

6.  Are  all  scales  in  place? 

7.  Have  the  scales  been  selected  and  placed  in  the  best  possible 
manner? 

8.  Are  the  points  accurately  plotted? 

9.  Are  the  numerical  figures  for  the  data  shown  as  a  portion  of  the 
chart? 

10.  Have  the  figures  for  the  data  been  copied  correctly? 

11.  Can  the  figures  for  the  data  be  added  and  the  total  shown? 

12.  Are  all  dates  accurately  shown? 

13.  Is  the  zero  of  the  vertical  scale  shown  on  the  chart? 

14.  Are  all  zero  lines  and  the  100  per  cent  lines  made  broad  enough? 

15.  Are  all  lines  on  the  chart  broad  enough  to  stand  the  reduc:ion 
to  the  size  used  in  printing? 

16.  Does  lettering  appear  large  enough  and  black  enough  when 
seen  under  a  reducing  glass  in  the  size  which  will  be  used  for  printing? 

17.  Is  all  the  lettering  placed  on  the  chart  in  the  proper  directions 
for  reading? 

18.  Is  cross-hatching  well  made  with  lines  evenly  spaced? 

19.  Can  Ben  Day  work  be  used  advantageously  instead  of  cross- 
hatching? 

20.  Do  the  Ben  Day  shadings  selected  have  sufficient  contrast? 

21.  Are  all  instructions  for  Ben  Day  work  given  so  that  it  will  be 
impossible  for  the  engraver  to  make -a  mistake? 

22.  Are  dimension  lines  used  wherever  advantageous? 

23.  Is  a  key  or  legend  necessary? 

24.  Does  the  key  or  legend  correspond  with  the  drawing? 

25.  Is  there  a  complete  title,  clear  and  concise? 

26.  Is  the  drafting  work  of  good  quality? 


A    FEW    CAUTIONS  361 

27.  Have  all  pencil  lines  which  might  show  in  the  engraving  been 
erased  ? 

28.  Is  there  any  portion  of  the  illustration  which  should  be  cropped 
off  to  save  space  .^^ 

29.  Are  the  instructions  for  the  final  size  of  the  plate  so  given 
that  the  engraver  cannot  make  a  mistake? 

30.  Is  the  chart  in  every  way  ready  to  mark  "O.K"? 

The  English  language  has  a  grammar  with  hundreds  of  detailed 
rules  concerning  almost  every  possible  construction.  Though  graphic 
presentations  are  used  to  a  very  large  extent  to-day  there  are  at  present 
no  standard  rules  by  which  the  person  preparing  a  chart  may  know 
that  he  is  following  good  practice.  This  is  unfortunate  because  it 
permits  every  one  making  a  chart  to  follow  his  own  sweet  will.  Many 
charts  are  being  put  out  to-day  from  which  it  would  seem  that  the  person 
making  them  had  tried  deliberately  to  get  up  some  method  as  different 
as  possible  from  any  which  had  ever  been  used  previously.  Anyone 
of  us  would  be  thought  of  as  a  freak  instead  of  as  a  genius,  if  he  tried 
to  invent  his  own  constructions  for  the  English  language  and  to  place 
words  in  some  order  never  before  seen,  yet  many  persons  are  doing 
something  akin  to  this  when  they  attempt  to  present  data  by  some 
new  and  outlandish  method  of  charting.  Below  are  given  a  few  rules 
which  may  be  of  assistance  toward  getting  graphic  presentations  more 
on  a  standard  basis  so  that  they  may  be  instantly  read.  These  rules 
are  included  here  simply  as  suggestions,  and  they  should  be  considered 
as  only  tentative  until  such  time  as  definite  rules  have  been  agreed 
upon  and  sanctioned  by  authoritative  bodies. 

RULES  FOR  GRAPHIC  PRESENTATION 

1.  Avoid  using  areas  or  volumes  when  representing  quantities. 
Presentations  read  from  only  one  dimension  are  the  least  likely  to 
be  misinterpreted. 

2.  The  general  arrangement  of  a  chart  should  proceed  from  left  to 
right. 

3.  Figures  for  the  horizontal  scale  should  always  be  placed  at  the 
bottom  of  a  chart.     If  needed,  a  scale  may  be  placed  at  the  top  also. 

4.  Figures  for  the  vertical  scale  should  always  be  placed  at  the  left 
of  a  chart.     If  needed,  a  scale  may  be  placed  at  the  right  also. 

5.  Whenever  possible,  include  in  the  chart  the  numerical  data  from 
which  the  chart  was  made. 


362  GRAPHIC    METHODS 

6.  If  numerical  data  cannot  be  included  in  the  chart,  it  is  well  to 
show  the  numerical  data  in  tabular  form  accompanying  the  chart. 

7.  All  lettering  and  all  figures  on  a  chart  should  be  placed  so  as  to 
be  read  from  the  base  or  from  the  right-hand  edge  of  the  chart. 

8.  A  column  of  figures  relating  to  dates  should  be  arranged  with  the 
earliest  date  at  the  top. 

9.  Separate  columns  of  figures,  with  each  column  relating  to  a 
different  date,  should  be  arranged  to  show  the  column  for  the  earliest 
date  at  the  left. 

10.  \Yhen  charts  are  colored,  the  color  green  should  be  used  to 
indicate  features  which  are  desirable  or  which  are  commended,  and  red 
for  features  which  are  undesirable  or  criticized  adversely. 

11.  For  most  charts,  and  for  all  curves,  the  independent  variable 
should  be  shown  in  the  horizontal  direction. 

12.  As  a  general  rule,  the  horizontal  scale  for  curves  should  read 
from  left  to  right  and  the  vertical  scale  from  bottom  to  top. 

13.  For  curves  drawn  on  arithmetically  ruled  paper,  the  vertical 
scale,  whenever  possible,  should  be  so  selected  that  the  zero  line  will 
show  on  the  chart. 

14.  The  zero  line  of  the  vertical  scale  for  a  curve  should  be  a  much 
broader  line  than  the  average  co-ordinate  lines. 

15.  If  the  zero  line  of  the  vertical  scale  cannot  be  shown  at  the 
bottom  of  a  curve  chart,  the  bottom  line  should  be  a  slightly  wavy 
line  indicating  that  the  field  has  been  broken  off  and  does  not  reach  to 
zero. 

16.  When  curves  are  drawn  on  logarithmically  ruled  paper,  the 
bottom  line  and  the  top  line  of  the  chart  should  each  be  at  some  power 
of  ten  on  the  vertical  scale. 

17.  When  the  scale  of  a  curve  chart  refers  to  percentages,  the  line 
at  100  per  cent  should  be  a  broad  line  of  the  same  width  as  a  zero  line. 

18.  If  the  horizontal  scale  for  a  curve  begins  at  zero,  the  vertical 
line  at  zero  (usually  the  left-hand  edge  of  the  field)  should  be  a  broad 
line. 

19.  When. the  horizontal  scale  expresses  time,  the  lines  at  the  left- 
and  right-hand  edges  of  a  curve  chart  should  not  be  made  heavy,  since 
a  chart  cannot  be  made  to  include  the  beginning  or  the  end  of  time. 

20.  When  curves  are  to  be  printed,  do  not  show  any  more  co- 
ordinate lines  than  necessary  for  the  data  and  to  guide  the  eye.  Lines 
3^-inch  apart  are  sufficient  to  guide  the  eye. 


A    FEW    CAUTIONS  363 

21.  Make  curves  with  much  broader  Hues  than  the  co-ordinate 
ruhng  so  that  the  curves  may  be  clearly  distinguished  from  the  back- 
ground. 

22.  Whenever  possible  have  a  vertical  line  of  the  co-ordinate  ruling 
for  each  point  plotted  on  a  curve  so  that  the  vertical  lines  may  show  the 
frequency  of  the  data  observations. 

23.  If  there  are  not  too  many  curves  drawn  in  one  field  it  is  desirable 
to  show  at  the  top  of  the  chart  the  figures  representing  the  value  of 
each  point  plotted  in  a  curve. 

24.  When  figures  are  given  at  the  top  of  a  chart  for  each  point  in  a 
curve,  have  the  figures  added  if  possible  to  show  yearly  totals  or  other 
totals  which  may  be  useful  in  reading. 

25.  Make  the  title  of  a  chart  so  complete  and  so  clear  that  misinter- 
pretation will  be  impossible. 

The  American  Society  of  Mechanical  Engineers  has  invited  about 
fifteen  of  the  societies  of  national  scope  in  America  to  co-operate  in  a 
Joint  Committee  on  Standards  for  Graphic  Presentation.  The  societies 
included  are  largely  societies  whose  members  have  extensive  use  for 
graphic  presentation  in  their  daily  work.  One  member  from  each 
society  will  be  on  this  committee.  It  is  hoped  that  the  committee  will  be 
able  to  recommend  a  small  number  of  brief  and  simple  rules  which  may 
be  used  as  a  sort  of  grammar  by  persons  who  have  graphic  presentations 
to  prepare  and  to  interpret.  Reports  from  this  joint  committee  should 
be  watched  for  so  that  any  rules  which  may  be  agreed  upon  may  be 
put  into  effect  as  soon  as  possible. 

Improvements  in  the  means  of  transportation  by  water,  rail,  auto- 
mobile, wire,  and  wireless  in  recent  years  have  caused  a  tremendous 
increase  in  the  amount  of  printed  matter  and  the  amount  of  statistical 
material  read  by  the  average  person.  Newspapers  and  magazines  are 
daily  presenting  more  and  more  statistical  information.  If  we  study 
the  subject  even  a  little,  it  will  be  seen  that  each  of  us  deals  daily  with  a 
vast  number  of  facts  of  a  quantitative  nature  which  could  preferably 
be  presented  in  graphic  form.  When  graphic  methods  are  more  widely 
used  for  portraying  quantitative  facts,  there  will  be  a  tremendous  gain 
to  accuracy  of  thought  as  well  as  a  great  saving  of  that  most  valuable 
thing  in  the  world — time. 

THE   END 


INDEX 


Abbreviations  for  chart  work,  345,  346 
Accidents,  as  affected  by  daylight,  140 

in  industrial  plants,  144,  145 

on  railroads  of  United  States,  134,  135 
Accountants,  viewpoint  of,  300 
Accuracv  and  significant  figures,  326 
Acker,  Merrall  &  Condit  Co.,  116 
Adding  machines,  pocket,  325 
Advertising,  bead  maps  for,  253 

maps  for,  238,  239 

use  of  curves  for,  77,  78 
Allen,  William  H.,  250 
American  Jersey  Cattle  Club,  278 
American  Machinist,  335 
American  Railway  Association,  349 
American  Review  of  Revieios,  46,  47,  229, 231 
American  Society  of  Mechanical  Engineers, 

ii,  31,  52,  54,  122,  363 
American  Statistical  Association,  167,  176, 

197 
American  Telephone  &  Telegraph  Co.,  5, 

179,  240,  309,  353,  354,  355,  356 
Analysis  of  sales,  188 
Angle  of  a  cumulative  curve,  150 

of  a  curve,  131 
Annalist,  the,  see  New  York  Times  Annalist 
Annual  reports,  corporation,  307 
Apples,  price  curves  of,  127,  128,  129 
Arithmetically  ruled  co-ordinate  paper,  132 
Atlas  of  the  U.  S.  Census,  see  Statistical 

Atlas 
Atomizer  for  spraying  ink,  57 
Authorization  for  curve  records,  284 
Automobile  exports  of  United  States,  41, 43 

factory  records,  263 

factory  schedule  curves,  150 

sales  records,  255,  264 
Automobiles,  comparison  of,  347,  348 
Averages,  moving,  97,  283 

progressive,  153 

weighted,  103 

Babson,  Roger  W.,  120,  121 
Bacteria  in  river  water,  20 

in  river  water  at  varying  depths,  85 


Bald  Eagle  Valley  Railroad,  67 
Bar  diagrams  versus  curves,  310 
Bars  combined  with  a  curve,  54 

certain  made  prominent,  29,  30 

for  use  in  comparison,  22 

horizontal,  4 

horizontal,  representing  time,  53 

vertical,  46,  47 

vertical,  for  components,  138 
Bead  maps,  251 
Beads  for  map  use,  247,  248 

for  statistical  charts,  207 
Bell  Telephone  system,  353,  354,  355,  356 
Ben  Day  shading,  216,  220,  331,  332 

shading  on  maps,  209 

work,  331,  332 
Bertillon,  220 

Biologists,  use  of  curves  by,  203 
Biometrika,  202 
Blue-printing,  328 

cards,  259,  261 

curve  cards,  291,  296 

machines,  261,  296 
Boards  for  pin  records  of  costs,  191,  192 
Bonus  earned  chart,  52,  54 
Boston  Elevated  Railroad,  4 
Boston  Globe,  212 

Boston  Health  Department  Report,  30, 109 
Bowley,  Arthur  L.,  ii,  98 
Breaks  in  drawings,  190 
Bridges,  drawing,  upon  photographs,  209 
Brotherhood  of  Railroad  Trainmen,  103 
Building  construction  in  United  States,  120, 

121 
Buildings,  maps  for  showing  height  of,  220 
Bureau  of  Railway  Economics,  257 
Butter-fat  curves,  279 

Camera  lenses,  330 

Cameras,  motion  picture,  for  time  study,  50 
Campaigns,  political,  338 
Car-floats,  dispatching,  61,  62 
Cars,  shortage  and  surplus,  349 
Cardboard  for  blue-printing,  259,  261 
models,  336 


365 


366 


GRAPHIC    METHODS 


Card-sorting  machines,  322 
Cards  for  blue-printing,  259,  261 

for  curve-plotting,  256 

for  curves,  275 

for  tabulating  machines,  320 
Cards,  information,  287 
Carson,  John  M.,  326 
Cartoon  drawings,  20,  21 
Cattle  distribution  in  United  States,  215 
Cautions,  a  few,  344 

Celluloid-covered  tacks  for  maps,  247,  248 
Celluloid,  erasing  drawings  from,  210 

flags  for  maps,  247 

for  drawings  with  maps,  210 

for  mounting  maps,  210 

tacks  for  writing,  247,  248 
Cement  plants  in  United  States,  243 

price  of  for  thirty  years,  77 
Census  Abstract,  218 

Census  Atlas  of  United  States.     See  Statis- 
tical Atlas 
Census-Office  methods,  320,  321 
Census  tabulating  card,  320 
Charts,  best  size  for,  345 

in  political  campaigns,  338 

on  walls,  306 
Checking  list  for  graphic  work,  359,  360 
Chicago   Burlington   &   Quincy   Railroad, 

40 
Chicago  pin  map  for  population,  246 
Chicago  telephone  rates,  126 
Choice  of  scales,  352 

Cincinnati,  homes  of  factory  workers,  214 
Circle  and  sectors,  5 
Circles  compared,  36,  37 
Clamps  for  hanging  maps,  232 
Cleveland  Plain  Dealer,  92 
Cloak  and  suit  industry  in  New  York,  166 
Coals,  comparative  value  of,  88 
Coloring  maps,  209 
Color-printing,  5,  331 
Colors  for  chart  work,  57 
Columns  of  figures,  order  for,  45 
Combined  curves,  125 
Commerce  of  the  United  States,  70,  71 

of  the  world,  76 
Commercial  geography,  21 
Commercial  Museum  of  Philadelphia,  70, 

74,  76,  112 
Commission  on  Economy  and   Efficiency, 

33,  34 
Comparisons,  20 

involving  time,  36 
Comparison  of  curves,  107 
Compo-board,  232 


Component  parts,  1 

parts  grouped,  33 

parts  shown  by  curves,  138 
Compound-interest  curve,  131 
Conjugal  condition  of  population,  9 

of  population  of  United  States,  168,  169 
Construction  of  gi  aphical  charts,  335 
Co-ordinate  lines,  spacing  of,  362 

paper,  55 

paper  for  weekly  records,  150 

paper,  universal,  60 

ruling,  284 
Copper  production,  26 
Copying  drawings,  329 
Copyrights  on  maps,  237 
Cork  composition  for  map  mounting,  232 
Corn  crop  in  United  States,  44 

planting  dates  in  United  States,  213 

yield  and  rainfall,  124 

yield  per  acre  in  United  States,  217 
Corporation  directors,  289,  298 

executives,  28D 

financial  reports,  307 

record  department,  292 
Correlation,  129,  199 

definition  of,  199 
Corrugated  straw-board  for  map  pins,  191 
Cost  analysis  by  pin  boards,  191,  192 

of  handling  freight,  184,  188,  192 
Cotton  goods,  production  and  export,  74, 

75 
Cotton  production,  22 

production  and  export  of  United  States, 
41 
Country  Gentleman,  213,  215,  232 
Cows,  individual  record  curves  for,  278,  279 
Crayons  for  coloring  maps,  57,  221 
Crayons,  paraffin,  57 
Crests  and  valleys  of  curves,  79 

of  curves,  79 
Crop  Reporter,  100 
Cross-hatching,  9 
Cross-index  of  curves,  291 
Croton  water-supply  curves,  160 
Cumulative  curves,  149 

frequency  curves,  174,  176,  177,  182,  184 
Cunningham,  Wm.  J.,  132,  134,  135,  136 
Curtis  Publishing  Co.,  238 
Curve  comparison,  107 
Curve  plotting,  47,  69,  84 
Curves  and  vertical  bars,  47 

for  the  executive,  254,  288 

interpretation  of,  357 

inversely  related,  126 

plotted  on  cards,  259,  275 


INDEX 


367 


Curves  and  vertical  bars,  reading  of,  30£ 

serial  numbers  for,  287 

shown  by  reflectoscope,  303 

versus  bar  diagrams,  310 
Cycles  of  curves,  97,  283 

in  curves,  97,  283 
Cylindrical  lenses,  330 

Data,  7,  42,  88,  126,  178,  204,  243,  333 
Data  for  curves,  on  face  of  chart,  80,  258 

for  curves,  shown  on  chart,  80,  258 

included  in  a  chart,  24,  25,  26 
Dates,  position  of,  in  curve  charts,  72 
Davenport,  C.  B.,  ii,  164,  165 
Davis,  Pierpont  V.,  ii 
Day  &  Zimmermann,  296,  305,  306 
Death  rates  in  United  States,  174,  351 
Decreases  shown  graphically,  30 
Degenerative  diseases,  351 
Department  of  Agriculture  Field  Service, 

232 
Dependent  variable,  definition,  84 
Depressions,  financial,  104 
Dimension  lines,  5,  148 
Directors  of  corporations,  289,  298 
Dispatching  charts  for  trains,  61,  62,  67 
Display  fixtures  for  curves  and  maps,  305 

fixtures  for  maps,  233 
Distribution  charts,  165 

curves,  165 

of  wealth,  197 
Dividends  and  earnings  of  Steel  Corpora- 
tion, 313,  314 
Dixon,  Frank  Haigh,  115 
Dodd,  Mead  &  Co.,  250 
Dodge's  Advanced  Geography,  22 
Double  co-ordinates  for  curves,  95 

scales  for  curves,  95  ■ 

Draft  curves  for  water  consumption,  160 
Drawing  ink,  46,  47,  276 
Dreyfus,  Edwin  D.,  117,  118 
Drinking,  reduction  in,  345 
Droege,  John  A.,  Freight  Terminals  and 
Trains,  48 

Earnings  and  dividends  of  Steel  Corpora- 
tion, 313,  314 
of  college  graduates.  111 
of  wage  earners  in  U.  S.,  180,  181 

Earthwork  curves,  163 

Edison  Company,  New  York,   108,   138, 
140,  146 

Eggs,  price  of,  100 

Elderton,  W.  P.  &  E.  M.,  ii 

Election  returns,  methods  of  giving,  341 


Engineering  Magazine,  12,  14,  17,  18,  116, 

125,  246 
Engineering  News,  87 
Engineering  Record,  79,  119,  209,  210 
Equitable  Life  Assurance  Co.,  174,  175 
Errors  in  comparison,  20 
Ewerbeck,  Dr.,  225 
Exaggeration  due  to  scales  used,  353 
Examination  marks,  charting,  205,  206 
Executive  control  curves,  254,  288 
Executives  of  corporations,  289 
Exhibition  board,  232 
Exports  and  imports  of  United  States,  37 
Exports  from  the  United  Kingdom,  98 
Eye-catchers,  25,  26,  27,  123 

Factory,  147,  155,  180,  256 

Fan  tests,  335 

Farm-land  values  in  United  States,  218 

Farwell,  E.  S.,  335 

Figures  included  in  a  chart,  27 

misleading,  326 

significant,  326 
Files  for  curve  cards,  289,  291 
Financial  charts,  104 

prosperity  curves,  293 

reports,  corporation,  307 
Fire  losses  in  United  States,  120,  121 
Fisher,  Irving,  10 
Fixtures  for  displaying  curves  and  maps, 

305 
Flags,  celluloid,  for  maps,  247 
Flat-top  curve-plotting,  256 
Flood  curves,  77,  79,  119 
Food  prices  in  United  States,  103 
Football  games,  charting,  212 
Foreign  trade  of  United  States,  139 
Forms,  routing  printed,  18 
Formulas  for  curves,  202 
Frankfurt  a.M.,  Map  of,  225 
Freeman,  John  R.,  160 
Freight-car  shortage  and  surplus,  349 

handling,   curves   for   analysis   of,    184, 
188,  192 

service  on  Illinois  Central,  310 

service  on  Union  Pacific,  311 

traffic  density  map,  224 

train  operation,  123 
French  curves,  201 
Frequency  curves,  164 

Gang  punch  for  cards,  324 

Gantt,  H.  L.,  52,  54 

Garnett,  W.,  205,  206 

Gasoline  costs  for  motor  trucks,  198 


368 


GRAPHIC    METHODS 


Gasoline-electric  generator  advertisement, 

78 
Gear  teeth,  strength  of,  334 
General  Electric  Review,  78,  239 
General  methods,  321 
Geography  books,  22 
Gifford,  Walter  S.,  179,  240 
Gilbreth,  Frank  B.,  50 
Good  Housekeeping,  21 
Grammar  for  graphic  work,  361 
Graphic  presentation,  rules  for,  362 
Graphical  charts,  construction  of,  335 
Green  ink,  making  line  cuts  from,  330,  331 
Grolier  Society,  358,  359 
Grouping  of  component  parts,  33 
Grooves  in  cards  for  filing,  296 
Gummed  letters,  46 

tape  for  map  mounting,  231 

Half-tones  from  pin  maps,  235 
Handling  freight,  cost  of,  184,  188,  192 
Harriman,  Mrs.  E.  H.,  250 
Harvard  Engineering  Journal,  337 
Harvard  University,  212 
Harvard  University  graduates,  251 
Hazen  and  Whipple,  95 
Health-department  reports,  108 
Heating  and  Ventilati7ig  Magazine,  93 
Height  of  university  students,  165 
Hewes,  Amy,  167,  176 
Himman,  J.  J.,  114 

Hollerith  tabulating  machines,  229, 230, 231 
Holmes,  H.  W.,  208 
Horizontal  bars,  4 

for  comparison,  24 

representing  time,  53 
Hull,  G.  H.,  104 
Human  figure  in  comparisons,  39 

Illinois  Central  Railroad,  310 
Illusions,  optical,  358,  359 
Imports  and  exports  of  United  States,  37 
Incandescent-lamp  tests,  337 
Income  curves,  197 
Income  of  technical  graduates,  204 
Increases  shown  graphically,  30 
Independent,  the,  21,  38 
Independent  variable,  definition,  84 
Index  numbers,  100 

Indianapolis  Department  of  Health,  114 
Indianapolis  smoke  deposits,  245 
Industrial  depressions,  104 
Industrial  Engineering,  117,  118 
Infectious  diseases  shown  in  contrast,  30 
Information  cards,  286,  290 


Ink,  drawing,  46,  47,  276 
Internationale  Baufach-Ausstellung,  225 
Inversely  related  curves,  126 
Inverted  curves,  96 
Iron  Age,  the,  110,  119 
Irregular  curves,  use  of,  201 
Isometric  drawings,  333 
ruling,  167,  334,  335 

Japanese  road  signs,  346 
Jersey  Cattle  Club,  American,  278 
Jevons,  Stanley,  319 

Joint  Board  of  Sanitary  Control,  166,  253 
Joint  Committee  on  Standards  for  Graphic 
Presentation,  ii,  363 

Keuffel  and  Esser  Company,  326 
Key  for  charts,  360 
King,  Willford  I.,  ii,  328 

Labeling  packages,  90,  91 
Uamps,  types  in  use,  138 

tests  of  incandescent,  337 
Land  value  in  United  States,  218 
Lantern  slides  for  election  returns,  341 

slides  in  political  campaigns,  339 

talks  in  political  campaigns,  340 
Legend  for  charts,  360 
Lenses,  camera,  330 

cylindrical,  330 
"Less  than"  basis  for  frequency  curves,  179 
Lettering  on  charts,  26,  82 
Letters  of  appeal  for  money,  250 

gummed,  46 
Lighter  operation,  chart  for,  56 
Line  cuts  from  pin  maps,  234 

made  from  green  ink,  330,  331 
Line  thickness  in  reduced  drawings,  242 
Lines  connecting  different  bars,  31 
Loans  to  industrial  employees,  156 
Locomotive  feed-water  curves,  159 
Logarithmic  co-ordinates,  132 

paper,  334,  362 

ruling,  334 

scale  for  curves,  132 
Lorenz  curve,  197 
Lorenz,  M.  O.,  197 
Lubrication  cost  at  a  factory,  256 

Manufactured  products  of  cities,  23 
Map  and  pin  systems,  226 
Map  copyrights,  237 

models,  225 

pins,  225 

pins  used  for  cost  analysis,  192 


INDEX 


369 


Map  pins  with  numbers,  243,  247 

presentations,  208 

tacks,  225 
Maps,  coloring,  209 

for  corporation  records,  293 

for  election  returns,  341 

for  wall  use,  225,  229 

mounting  of,  231 

shading,  209 
Marx,  Guido  H.,  334 
Mass  curves,  149 
Massachusetts    Institute    of    Technology, 

11,  198 
Mazda  lamps,  337 
McAbee,  William  D.,  245 
McGraw-Hill  Book  Co.,  335 
Mechanical  shading,  331,  332 
Merchant  tonnage  of  United  States,  112, 

113 
Methods,  general,  321 

Metropolitan  Sewage  Commission,  20,  85 
Milk-analysis  curves,  114 
Milk-production  curves,  278,  279 
Misleading  figures,  326 
Mode,  165,  170 
Models,  card-board,  336 

solid,  336 
"More  than",  basis  for  frequency  curves, 

179 
Morgan,  J.  P.  &  Co.,  15 
Motion  picture  cameras  for  time  study,  50 
Motor,  346,  347 
Motor  trucks,  cost  for  gasoline,  198 

cost  of  operating,  11 
Mount  Holyoke  College,  167,  176 
Mounting  maps,  231 
Moving-average  curves,  97,  283 
Municipal  parades,  343 

record  departments,  298 
Muslin  facing  for  pin  boards,  231 

Naphtaly,  Sam.  L.,  122 
Natural  scale  for  curves,  132 
Need  for  graphic  methods,  1 
Newark,  N.  J.,  public  schools,  2 
Newburgh,  N.  Y.,  report  on  schools,  24 
New  York  Edison  Company,  108,  138,  140, 

146 
New  York  municipal  parade,  343 
New  York  Public  Library,  299,  329 
New  York  Times  Annalist,  13,  45,  313,  350 
New  York  Times,  120,  121,  222,  351 
Newspaper  circulation  curves,  92 
Nippon  Automobile  Club,  346 
Numbered  map  pins,  243,  247 


Optical  illusions,  80,  81,  358,  359 
Order  of  Railroad  Conductors,  103 
Orders,  routing,  19 
Organization  charts,  14,  15 
Orrok,  George  A.,  201 

Panics,  financial,  104 

Parades,  charts  shown  in,  342,  343 

municipal,  343 
Paraffin  crayons,  57 
Paris,  height  of  buildings  in,  220 
Paris,  plaster  of,  336 
Passengers  carried  on  railways,  39 
Passenger  service  on  Union  Pacific,  312 
Payroll  curves,  260 

record  curves,  276 
Peaked-top  curves  plotting,  256 
Peaks  of  curves,  99 
Pearson,  Karl,  202 
Peddle,  John  B.,  335 
Pencil  lines,  erasing,  361 
Pennsylvania  Farmer,  124,  127,  128 
Pennsylvania  Railroad,  308 

profile  of,  213 
Percentage  scales  for  curves,  132 
Perspective  routing  charts,  19 
Philadelphia  Commercial  Museum,  70,  74, 

76,  112 
Philadelphia  Transit  Commissioner,  245 
Philip's  Chamber  of  Commerce  Atlas,  26, 

27 
Philippines,  comparative  size  of,  211 
Photographing  bead  maps,  252 

pin  maps,  230,  234 
Photographs,  drawing  upon,  209 

progress,  49,  50 

used  with  maps,  209 
Photostat,  the,  296,  330 

use  of,  329 
Pin  boards  for  cost  analysis,  191,  192 
Pin  maps  to  scale,  246 
Pins  for  map  use,  225 

for  population  density  on  maps,  221 
Pipe,  cast-iron,  110 

Pittsburgh  &  Lake  Erie  Railroad,  81,  82 
Plant,  Thomas  G.&  Co., advertisement,  233 
Plaster  of  Paris,  336 
Plates,  weight  of  steel,  333 
Pneumonia,  deaths  from,  at  different  ages, 

172,  173 
Polar  co-ordinates  for  curves,  80 
Political  campaigns,  charts  in,  338 
Popular  Science  Monthly,  164,  165 
Population  curves,  130 

density  maps,  221 


370 


GRAPHIC    METHODS 


Portland,  Oregon,  208 

Power  development  in  United  States,  239 

Presidential  election  analysis,  10 

Princeton  graduates,  class  of  1901,  73 

Princeton  University,  111 

Production  schedule  curves,  150 

Profile  drawings,  211 

Progress  photographs,  50,  51 

Progressive  averages,  153 

Prominent  bar  for  contrast,  30 

Prout,  Curtis,  ii 

Proportions  of  charts,  355,  356 

Prosperity"  charts,  104 

Prussia,  distribution  of  wealth  in,  197 

Pujo  Money  Report,  13 

Punched-card    tabulating   machines,    320, 

321,  322,  323,  324 
Purchasing-department  curves,  293 

Queen  Quahty  shoes,  advertisement,  233 

Races  in  population  of  the  world,  4 
Railway  Age-Gazette,  115,  142,  224 
Railroad  annual  reports,  309 

earnings  in  United  States,  115 

operating  costs,  142,  143 
Rank  charts,  32,  63,  65,  66 
Rea,  Samuel,  308 
Record  departments  for  cities,  299 

room  for  corporations,  292 
Records  for  the  executive,  288 

needless,  285 
Rectangular  co-ordinates,  132 
Reduction  of  earnings,  329,  330 
Reducing  glass,  use  of,  241,  329 
Reduction  in  size  of  drawings,  241 
Reflecting  lantern  for  curves,  303 
Reflectoscope  for  curves,  304 
Reports  of  corporations,  307 
Returns,  election,  341 

Revenues  of  railroads  of  United  States,  257 
Review  of  Reviews,  46,  47,  229,  231 
Rittenhouse,  Elmer,  175,  351,  352 
Road  signs,  Japanese,  346 
Roads  in  New  York  State,  map,  222 
Routing  charts,  17 
Routing  of  papers  in  an  office,  34 

salesmen,  236 
Royal  Statistical  Society,  205,  206 
Rule,  slide,  326,  328 
Rules  for  graphic  presentation,  361 
Russell  Sage  Foundation,  24,  32,  33 

St.  Louis  &  San  Francisco  Railroad,  224 
Sales  analysis  curves,  188,  269 


Sales  records  by  tabulating  machines,  324 

record  map,  223 
Salesmen,  chart  for  ranking,  63 

routing  of,  by  pins,  226 
San  Francisco  fire,  120,  121 
"Satellite  Cities",  214 
Saturday  Evening  Post,  238 
Savings-banks  deposits  in  United  States, 

350 
Scale  arrangement  for  charts,  362 
Scales,  choice  for  horizontal  and  vertical, 
352 

double,  for  curves,  79 

for  charts,  8 

on  charts,  rule  for,  211 
Scallop  shells,  164 

Schedule  curves  for  factory  output,  150 
Schools  of  the  United  States,  32 
Scientific  American,  the,  29 
Scott,  Roscoe,  E.,  337 
Seaboard  Air  Line  Railway,  177 
Sections  omitted  from  drawings,  190 
Serial  numbers  for  curves,  286 
Shading,  Ben  Day,  331,  332 

mechanical,  331,  332 
Sheffield  Scientific  School,  111 
Shipping  of  various  countries,  24 
Ships,  length  of,  49,  51 
Shot-gun  diagrams,  201 
Significant  figures,  326 
Simple  comparisons,  20 

involving  time,  36 
Slide  rule,  use  of,  326,  328 
Slope  of  curves,  130,  131 
Smoke  deposits,  measuring,  245 
Smooth  curves,  118,  119,  201,  357 
Smoothing  curves,  98 
Solid  models,  336 
Soot  deposits,  measuring,  245 
Sophie  19tli,  milk  record,  278 
Spot  maps,  246 
Standard  corporation,  334 
Standards  for  graphic  presentations,  363 
Statistical  Atlas,  8,  28,  36,  65,  80,  130,  168, 

172,  215 
Statisticians  for  corporations,  293 
Steam,  cost  of  producing,  12 
Steam  turbine,  tests  of,  122 
Steel,  curves  for  strength  of,  119 
Steel  plates,  weight  of,  333 
Stockholders  of  corporations,  number  of,  308 
Storage  capacity  curves,  159 
Straw-board  for  mounting  maps  for  pins, 
230 

for  use  with  map  pins,  191 


INDEX 


371 


Street-car  service  map,  225 

String  for  routing  salesmen,  237 

Stream  velocity,  87 

Swazey,  Edward  Scott,  ii 

Subdivision  of  components,  8 

Suffern  &  Son,  30,  213 

Survey,  the,  6,  245 

Swinging  display  fixtures  for  maps,  233 

Symbols  for  charts,  345,  346 

System,  15,  90,  123,  223. 

Tabulating  Machine  Company,  322,  323, 

324,  325 
Tabulating  machines,  320,  321,  322,  323, 
324 

machines  for  cards,  323 
Tacks,   celluloid-covered,   for   maps,    247, 
248 

map,  225,  247,  248 
Tarr   and  McMurray's   new   geographies, 

22 
Taylor,  Graham  Romeyn,  214,  221 
Telephone  load  curves,  108 

rates,  126 

service  curves,  179 

service  in  Wisconsin,  178 
Telephones    in   United   States,   pin   map, 
240 

number  used  in  United  States,  354 
Temperature  curves,  117,  118 
Thompson,  A.  T.  &  Co.,  reflectoscope,  303 
Thomson,  H.  F.,  198 
Three-dimensional  charts,  205,  206 
Time  charts,  53 
Time-distance  charts,  64,  67 

curves,  64,  67 
Titles  for  charts,  344,  345 
Topographical  maps,  235 
Totalizing  curves,  125 
Tracing  cloth  used  with  maps,  210 
Trading  centers  in  United  States,  238 
Train-dispatching  charts,  61,  62,  67 
Train-operation  curves,  123 
Transparentizing  solution,  328 
Trenton,  N.  J.,  public  schools,  2 
Trucks,  costs  for  gasoline,  198 

cost  of  operating,  29 
Tuberculosis  death  rates,  351 
Tug-boat  operation,  58 
Turbine,  steam,  tests  of,  122 
Two  independent  variables,  charts  for,  205, 
206 


Union  Bag  &  Paper  Co.,  45 

Union  Pacific  Railroad,  311,  312 

United  States  Census  Office  methods,  320, 

321 
United  States  Steel  Corporation,  313,  314 
University  of  Cincinnati,  46,  47,  229,  231 

Vacation  ch  art ,  5  3 
Variables  for  curves,  84 
Variables,  two  independent,  333 
Velocity  of  water  in  streams,  87 
Vertical  arrangement  of  curves,  347,  349 

bar  charts,  354 

bars,  46,  47 

for  components,  138 

Wage  charts,  180,  181,  182 

comparison  on  railroads,  49 
Wall  board,  232 

charts,  306 

exhibits,  358 

maps,  225,  229 
Wall  Street  Journal,  308 
Warne,  Frank  J.,  103 
Water  power  in  United  States,  216 
Water  storage-capacity  curves,  159 
Wave  lengths  on  curves,  283 
Waves  in  curves,  97 
Wavy  line  for  bottom  of  chart,  350,  352, 

362 
Weather  cnarts,  93 

Wealth,  curves  showing  distribution,  197 
Weight  of  steel  plates  chart,  333 
Weighted  averages,  103 
Westinghouse   Electric    &   Manufacturing 

Co.,  295 
Westinghouse,  George,  31 
Wheat,  production  of,  1910,  27 
Wheeling  &  Lake  Erie  Railroad  ^  02 
Whipple,  George  C,  95 
White,  WiUiani  Pierrepont,  222 
Worcester  Polytechnic  Institute,  204 
World's  Work,  the,  39,  40,  43,  49,  51,  211 
Worsted  mill  operation,  52,  54 

Yale  University,  111,  212 

Years,  methods  for  naming  on  curves,  82 

Yule,  G.  Udny,  ii 

Zero  lines  for  curves,  82,  140,  350,  351,  352 
Zero  lines  on  curve  cards,  271 
Zizek,  Franz,  ii 


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